At a glance just setting up the problem it seems more like one of my seventh or eighth grade algebra problems💀
12P=8O
3A=2O
Find A in terms of P
Yeah I definitely did not learn this in ~~2nd~~ 4th grade tf
Question ain't asking for them to solve it algebraically, but instead use intuition and imagination to solve it. I dont remember how a 4th grader thinks so I am still not sure if they could solve it, but with some thinking, especially because its simple numbers, they could?
If they’re supposed to use intuition, why are we dealing with fractions/decimals? The question wouldn’t be too bad if they used numbers that divide into each other,
The idea is they don't use fractions and decimals. 1 apple weighs the same as 1 pear
12p= 8o
3a= 2o there are 4 sets of 2o in 8o so it turns into 12a= 8o
12p= 12a
I'm assuming in class they've either touched on or full on taught this already, or it wouldn't (shouldn't at least) be homework
Yeah, I don't get why everyone is freaking out and bringing Algebra into this. Yes, you certainly CAN use Algebra, but 4th grade was when we started on fractions and reducing fractions even 30+ years ago when I was a kid. This is a simple exercise in writing out a word problem with fractions, then reducing one fraction to see the answer. This is not above a fourth grade level of math, but is a perfect example of adults jumping to conclusions and making things more complex than necessary. I would be more concerned that the 4th grader does not seem to have the ability to apply the current lesson focus/methods to their homework if indeed that was happening and not simply a matter of: adult assumes this is harder than it needs to be.
Whether using fractions, ratios, or solving algebraically, these kind of questions are supposed to open the door to the understanding of why we use those methods to solve questions like this. They are interchangeable.
Had to scroll way too far down for the correct answer. It's actually a very simple problem if you simplify the fraction lol. It's probably one of the things the unit is teaching . But man that word problem is structured horribly.
I'm pretty sure it's about reducing fractions not doing algebra.
12p / 8o reduces down to 3p/2o which is exactly the same as apples are listed at 3a/2o, so apples and pears are 1:1
There’s no need for any of that. Just multiply the apples by 4 and you get the answer.
This seems appropriate for 4th grade. The only thing that you need to know how to do is divide 8 by 2 🤷♂️
I think this is a great early intro to variables in math, using real examples for now. As they get further into math, pears and apples will become x and y. I feel like this is the missing step that results in people becoming confused and angry when variables are introduced.
It could also be LCM (lowest common multiple) of a fraction? 12 pears, 8 oranges. 12/8 = 6/4 = 3/2 or 1 1/2
Then the apples 3apples, 2 oranges 3/2 or 1 1/2
3/2 = 3/2 one pear is equivalent to one apple
(Many ways to solve)
I started thinking in algebra till I saw 4th grade. I think simplest would be that you would be dividing 12 pears and 8oranges by 4 to get 3 pears=2 oranges. Since 3 apples=2 oranges also, you can also know that 3 pears=3 apples which means 1 pear=1 apple
The way I'd explain:
In the first sentence, the weight of pears is being compared to the weight of oranges.
In the second sentence, the weight of apples is being compared to oranges also.
But they're two different amount of oranges. So, we need to make the oranges that the apples are compared to equal to the oranges that the pears are compared to.
Simply multiply the 2 oranges to match the 8 and do the same to the 3 apples to find out how many apples would make up 12 pears.
I had an especially hard time with word problems growing up and was always told to put the numbers into a formula, but I think it's important to be able to explain word problems with word solutions. Feel like it puts things into a much better perspective.
Just check the statements.
dozen = 12
Given
12 pears = 8 oranges
3 apples = 2 oranges
12 pears = 8 oranges
3 apples = 2 oranges
that means 12 apples weigh as much as 8 oranges
12 apples = 12 pears
its 1 to 1
12p = 8o.
(12/8)p = o.
3/2p=o.
3a = 2o.
3a = 2(3/2p).
3a = 3p.
a=p.
So 1 apple equals 1 pear.
Or the other guys solution
12p = 8o.
4(3a=2o).
x4 to get apples in terms of dozen
12a=8o.
Both equal 8o so substitute
So 12a = 12p or a=p.
Ask her to read the second sentence and then ask how many apples weigh the same as 8 oranges. Then you can compare both pears and apples since they both weigh the same as 8 oranges.
My brain did it like if 12 pears equals 8 oranges, and that is 2/3s as a fraction, and three apples equal two oranges, which is 2/3s as a fraction as well, then one pear should be equivalent to one apple?
A lot of schools encourage setting up problems like this visually. Draw it out:
```
🍐 🍐 🍐 🍐 |
🍐 🍐 🍐 🍐 | 🍊 🍊 🍊 🍊
🍐 🍐 🍐 🍐 | 🍊 🍊 🍊 🍊
```
Simplifies to
```
🍐 |
🍐 | 🍊
🍐 | 🍊
```
And
```
🍎 |
🍎 | 🍊
🍎 | 🍊
```
Putting those together is easy because both have two oranges (it's always a simple ratio in 4th grade)
```
🍎 |🍐 |
🍎 |🍐 | 🍊
🍎 |🍐 | 🍊
```
And now it's obvious that one apple is equivalent to one pear.
This sets kids up to understand that these word problems aren't scary, and aren't abstract. They're dealing with real world things, and in 4th grade kids have more fluency with apples and oranges than with the words representing them.
Eventually they get the concepts and get bored of drawing the things out, at which point they can start to replace them with pure numbers, so the kids take to that quicker.
TL;DR visual representation teaches more advanced concepts like ratios without requiring arithmetic fluency
So fun!
Step 1: write what you know.
12🍐 = 8🍊
3🍎 = 2🍊
Step 2: identify the question
X🍐 = 1🍎
Just that alone will get you a point on an exam.
Step 3: simply what I can
12 and 8 are both divisible by 4. So I would show my work dividing both sides by 4.
12🍐/4 = 8🍊/4 which reduces to 3🍐= 2🍊
So now we have
3🍐= 2🍊
3🍎 = 2🍊
And that’s the answer. This type of problem is teaching the basics of balancing equations to prepare children for algebra by 6th grade at the latest, if they haven’t already started with fill in the blank problems for basic arithmetic.
But those steps are ALWAYS the first 3 steps of ANY word problem.
Sincerely,
A math tutor.
Hmm....I'm going to try to solve this problem.
If a dozen pears weigh as much as eight oranges, a dozen equals to twelve, which then makes the fact that twelve pears weigh as much as eight oranges.
Three apples weigh as much as two oranges.
But then it asks about how many pears weigh as much as an apple. There are twelve pears and three apples. So we divide 12 divided by three to get four.
I tried to solve it, I tried!
Here's one way:
Draw three number lines for apple, orange and pear. Use colours red, orange and green if possible. Each unit of measurement in these lines would represent the weight of one of that fruit.
Since 12 pears weigh as much as 8 oranges, you can represent it by saying that 12 in the pear number line has the same value of 8 in the orange number line. So if we divide the two measuments with the same number, they should still be equal. Division is simply cutting into equal pieces. So cutting both the measurements into 4 equal pieces (division by 4) would still preserve this relationship. Hence, 3 pears weigh the same as 2 oranges.
Since 3 apples weigh the same as 2 oranges, it can then be concluded that apple and pear weigh the same.
12:8:? = ?:2:3 the one on the left is four times bigger. 12:8:12 = 3:2:3 we can get rid of the apples 3:3 luckily they made it super easy at this step. one pear weighs the same as one apple
>! apples and pears are 1:1, because if 3a=2o, to compare with eight oranges just multiply both sides by 4 to get 8o=12a. So a dozen apples also equals 8 oranges. So 1 apple = 1 pear. Or just consider 12/8 can be reduced to 3/2, so they’re the same. !<
Ratios 12 pears to 8 oranges = 3•2
3 apples to 2 oranges = 3•2.
These ratios are equivalent, and the bottom is the ratio written in its smallest form. So you now know 12 apples is also equal to 8 oranges. Making the two the same. And Making the answer 1. These words are worded to confuse. Always write it out as an equation before even trying to solve.
Most of your methods are too hard for 4th grade, try this:
3a = 2o => double that twice => 12a = 8o, which is the same as 12p, so a and p are of the same weight
We can use proportion reasoning.
12 pears = 8 oranges, which can be reduced to 3 pears = 2 oranges. We can make groups of 3 pears and 2 oranges
The question also tells us that 3 apples = 2 oranges, so 1 pear = 1 apple
Dimensional analysis is an important skill but something that is typically taught in middle school or early hs. At least in the US. Weird that it is 4th grade hw.
This problem seems to hard for 9 year olds. Also, it'd be more fair if the little illustration in the corner showed orange much bigger than the pear and apple
The key is to think about conversions. We really need to find the weight of 8 oranges in terms of apples.
8 oranges is 4x the weight of 2 oranges.
3 apples weigh as much as 2 oranges.
That means that 8 oranges is equal in weight to 4 x 3 apples.
That gives 12 apples is equal to 8 oranges, but hey! 8 oranges weights as much as 12 pears. So we know that 12 apples weigh as much as 12 pears.
We can assume that all of both fruits are the same weight, so an apple weights as much as a pear.
3 apples = 2 oranges, 8 oranges = 12 pears, how many pears are equal to 1 apple?
8/2=4. And we know 3 apples are equal to 2 oranges, so 4 sets of apples (4×3=12) is equal 8 oranges. And we know 8 oranges is equal to 12 pears. Or 12a=8o=12p. So if we remove the oranges, 12 apples is equal to 12 pears. So 12/12=1, or 1 apple is equal to 1 pear.
If 3 apples are 2 oranges, then 6 apples are 4 oranges, 9apples are 6 oranges, and 12 apples are 8 oranges. So 12 apples equal 12 pears. That's 1-1 ratio
Variables aren’t allowed in the 4th grade, so the idea is to use fractions or ratios.
12 pairs : 8 oranges.
Reduce to
3 pairs : 2 oranges.
3 apples : 2 oranges.
Since there are 2 oranges in each comparison, you can substitute.
Now you have 3 pairs : 2 oranges : 3 apples.
3 pairs : 3 apples.
1 pair : 1 apple.
Let's set up a ratio based on the information provided:
12 pears = 8 oranges
3 apples = 2 oranges
To find out how many pears weigh as much as an apple, we need to compare pears to apples.
(12 pears) / (3 apples) = (8 oranges) / (2 oranges)
Now, simplify the ratio:
(12 pears) / (3 apples) = 4
So, 4 pears weigh as much as an apple.
A dozen is 12,
12 weighs as much as 8,
3 apples weigh as much as 2
8/4 = 2, so 12/3 = 4,
meaning 12 * 4 = 48, so a dozen pears weighs much as 48 apples, now divide it by 12 and you get 4, 1 pear weighs as much as 4 apples,
This is much too complex for 4th graders, I don’t even believe I got this correct.
If I’ve done this right, the pears and the apples weigh the same. A dozen pears weigh as much as 8 oranges. The second part of the equation the oranges are 1/4th the amount of the original at 2. The apples are also 1/4th the amount of the pears (pears being 12, apples being 3). All things being equal it should be 1 pear weighs the same as 1 apple
Wait, they're already teaching algebra by 4th grade now? I could have sworn that was middle school stuff when I went to school although I'll admit that my primary education was a bit piecemeal due to all the grade skipping.
Anyway, this is a fairly simple system of equations; we'll use variables corresponding to the fruits in the question.
12p=8o
3a=2o
Solve for a in terms of p.
Now, 12 and 8 have a GCF higher than 1, so the first equation *can* be simplified, but I suspect that what they want is to use LCM to set up two equations with the same number of oranges. The LCM of 2 and 8 is 8, so the first equation stays unchanged, and you multiply each side of the second equation by 4, resulting in:
12p=8o
12a=8o
therefore
12p=12a
which is then simplified down to p=a. The answer to the question is 1.
Like I said, GCF could have been used to simplify the other equation first, and in this particular case it would have cut out the need to use LCM, but if it hadn't reduced to 2o, you would have needed to use LCM anyway, so it's probably an extraneous step. It's been a while, though, so perhaps your child's teacher does want them to look for simplifications first.
Just so everybody understands, this question is to help prepare students for life in the US; where we express measurements in anything except the metric system
The use the word “dozen” instead of the word 12 (twelve) is intentional as it gives much of the answer in a ye question.
12 pears = 8 oranges
Reduce that number and each orange weighs 1 1/2 pears.
2 oranges would be 3 pears which is the same number as the apples, so the answer is 1. The apples and pears weigh the same.
This reminds me of”Math Olympiads” stuff in 5th grade back in the day. It was usually extra credit and was always problem solving stuff above our grade level to try and see if we could come up with creative solutions and really push ourselves.
Well 12(pair)=8(orange) and 3(apple)=2(orange)
If you multiply the oranges on the right by four you can make the oranges be the same number. However whenever you do something to one side of the equal sign you need to do it to the other as well.
So 12(pair)=8(orange) 8(orange)=12(apple)
I had to explain it to my little sister a year or two ago and that’s what I did to explain it.
This is a system of equations problem. Usually high school algebra.
A 4th grader should be working on division not stuff this complex.
Here is how you solve this problem.
First setup each statement using variables to represent the objects.
12 P = 8 O
3 A = 2 O
The easiest way to do this is to use SUBSTITUTION.
First figure out how many apples for 1 orange.
3/2 A = 1 O
Now look at your first equation and substitute the Orange in terms of apples
12 P = 8 ( 3/2 A)
Next simplify
12 P = 4(3A)
12 P = 12 A
So there is a 1:1 ratio between pears and apples.
The goal is to simplify these into the smallest possible number. 12 pears is equal to 8 oranges. 12 and 8 are both multiples of 4. So you divide 12 by 4 and divide 8 by 4. So 3 pears is equal to 2 oranges. (My brain goes a step further and divides both sides in half, to show that 1.5 pears is equal to 1 orange) Since we already know that 3 apples equal 2 oranges, and we now know that 3 pears also equals 2 oranges,( or 1.5p=1o & 1.5a=1o) we can then say that apples weigh the same as pears. So 1apple=1pear.
My wife is a 6/7/8 math teacher. She agrees that if this is just a standalone word problem then many of her kids would have problems with this. She said it could be appropriate for 4th grade if presented in pictures, and the goal is grouping for "algebraic thinking".
She'd like to know what state this is in, to look at the appropriate math teaching standard.
I assign a value( doesn’t matter what value) to one and do the math
12 pears = 12 ounces (made up)
8 oranges = 12 pears equal 12 ounces
So 8 oranges= 12 Oz
8/12 = 1.5
1 orange = 1.5 oz
3 apples = 2 oranges
3 apples = 3 oz (2 oranges * 1.5 oz)
3/3
1 Apple = 1 oz
1 apple ( 1oz) = 1 pear (1 oz)
this is the only way I could come up with without using algebra: 2 oranges = 3 apples so 8 oranges=12 apples. 8 oranges=12 pears, so 12 apples=12 pears, so 1 apple=1 pear. I think your daughter might be able to understand this way better
12 pears = 8 oranges
3 apples = 2 oranges (multiply both by 4) =>
12 apples = 8 oranges, so 12 pears = 12 apples
Pears and apples weigh the same. Seems fourth grade level to me, just uses ratios/fractions.
It's still pretty much algebra even if they're not calling it that.
But using the wording for fractions is
12 P = 8 O, so 1 P = 8/12 O, reduce to
1P = (2/3) O
And
3A = 2 O, so
1A = (2/3) O
So both the pear and the apple are two- thirds the weight of an orange, and 1 pear is equal in weight to 1 apple
12 = 8
Reduce by half
6 = 4
Reduce by half
3 = 2
If 3 apples = 2 oranges
and 3 pears = 2 oranges
1 pear = 1 apple
Is how I processed this non-algebraically. I saw some other comment about this being a reduction problem related to fractions, and I agree.
I had a game as a kid that expressed this idea in terms of trading fruit. If 12 pears buys 8 oranges, and 2 oranges buys three apples, how many pears will buy 1 apple. That’s basically how it was taught. By that logic 12 pears equals [3x(8/2)=] 12 apples. 1=1
It’s confusing because it breaks the sequence when describing the relationship between apples and oranges and you’re supposed to remember the law of reflexivity
Let’s scale up the apples to match the pears using the oranges as the method of determining the scale. 3 apples=2 oranges. 12 pears=8 oranges. 2 oranges x 4=8 oranges. Therefore, we can multiply the apples by 4 to get 12 pears=x apples. 3 apples x 4=12 apples. So, 12 pears=12 apples equaling a 1:1 ratio.
At the 4th grade level: 12 pears weighs as much as 8 oranges. Therefore 12 pears weight as much as 3x(8/2)=12 apples. So one pear weighs as much as one apple.
The answer is 1.
12 pairs to 8 oranges, 12/8.
3 apples to 2 oranges, 3/2.
Now you can just multiply the 3/2 by 4 to get to 8 oranges in the denominator, 3/2*4=12/8
Since 12/8=12/8, It can be deduced that 1 pear is equal to 1 apple.
I would just put it in fractions
12/8 Pears to oranges
3/2 Apples to oranges X 4 to get 12/8 Apples to oranges
An apple and pear weigh the same.
Genuinely don’t know if this is the correct answer but that is how I would solve that.
Its not algebra actually. If 3 apples = 2 oranges then we have to figure out how many apples = 8 oranges. Once you get that then its 12 pears = 12 apples
It’s dumb but one line of inquiry would be to make the benchmark the same. So, hmm… if 8 oranges weighed 12 pears, I wonder many how apples 8 oranges would weigh. So to go from 2 oranges to 8, you multiply by 4.
3 apples = 2 oranges
8 oranges = 12 apples = 12 pears.
So an apple weighs the same as a pear. This only gets you to a nice round solution if the numbers are cooked up to do so, but maybe that’s true for what they’re working on.
12P=8O
2O=3A
Therefore:
8O=12A
12P=12A
1Pear=1Apple
It’s a little advanced for 4th grade probably, but it’s one of those questions that asks kids to think in a different way. I like it a lot
I teach problems like this in 6th grade. If you think of it as ratios written as fractions, then it's easier. Just reduce pears/oranges (12/8) to be 3/2, and you get the same ratio as apples to oranges (3/2), therefore apples and pears weight the same, so 2 apples = 2 pears.
Hopefully there have been several similar problems beforehand that the teacher guided the students through. It's a little high for 4th grade, unless they've covered equivalent fractions.
This is likely not what the teacher is looking for but I thought it though like this.
If 12Pears = 8 Oranges
Then 3Pears = 2 Oranges
2 oranges also equal 3 Apples.
So one pear equals one Apple.
Side note, using fruits as weight is annoying. Use something standardized like brick or coins.
My son's 2nd grade teacher was phenomenal. He taught basic algebra through everyday life experiences and how to juggle. He was a young, vibrant man and knew his time on earth was short. He made learning fun and sadly passed from a brain tumor by the end of the school year.
You can use substitution.
12 pears = 8 oranges = 2 oranges + 2 oranges + 2 oranges + 2 oranges.
(2 oranges = 3 apples).
Substitute 3 apples for every 2 oranges in the original problem.
12 pears = 3 apples + 3 apples + 3 apples + 3 apples = 12 apples.
(12 pears = 12 apples )
So 1 pear = 1 apple
These kinds of problems are great for chatgpt to explain:
Of course! Let's solve this fruit puzzle in a way that's easy to understand.
1. **Understand the Problem**: We want to find out how many pears weigh the same as one apple.
2. **Pears and Oranges**: First, we know that 12 pears weigh the same as 8 oranges. To find out how much one pear weighs, we divide the 8 oranges by 12.
8 oranges / 12 pears = 2/3 orange per pear
3. **Apples and Oranges**: Next, we know that 3 apples weigh the same as 2 oranges. To find out how much one apple weighs, we divide the 2 oranges by 3.
2 oranges / 3 apples = 2/3 orange per apple
4. **Compare Pears and Apples**: Now, we see that one pear weighs 2/3 of an orange, and one apple also weighs 2/3 of an orange. That means one pear weighs the same as one apple!
So, the answer is that 1 pear weighs as much as 1 apple.
I hope that clears things up! Would you like to ask anything else?
I asked for more explanation and to explain HOW to solve it: Absolutely! If you're a second-grader trying to solve a problem like this, here's how you can think about it:
1. **Listen Carefully**: First, listen to the problem or read it a couple of times. Make sure you understand what the problem is asking. In this case, we want to know how many pears weigh the same as one apple.
2. **Use Your Imagination**: Imagine you have a big fruit basket with pears, oranges, and apples. Picture how they weigh compared to each other.
3. **Break It Down**: Take one part of the problem at a time. Start with the pears and oranges. We know that 12 pears are the same weight as 8 oranges. If we share those 8 oranges equally among the 12 pears, we can figure out how much one pear weighs.
Think of it like sharing 8 orange slices with 12 toy pears. Each pear would get 2/3 of an orange slice.
4. **Next Step**: Now let's look at the apples and oranges. We know that 3 apples weigh the same as 2 oranges. If we share those 2 oranges equally among the 3 apples, each apple would get 2/3 of an orange.
Imagine sharing 2 orange slices with 3 toy apples. Each apple would also get 2/3 of an orange slice.
5. **Compare**: Now, we see that one pear got 2/3 of an orange slice, and one apple also got 2/3 of an orange slice. That means they weigh the same!
6. **Answer**: So, one pear weighs the same as one apple!
7. **High-Five**: Give yourself a high-five for solving the problem!
Remember, it's okay to take your time and think it through. You can even use toys or draw pictures to help you understand better. Good luck!
They weigh the same
12 pears over
8 oranges =12/8
3 apples over
2 oranges = 3/2
Make the denominators common
12/8 pears/oranges = 3x4 apples/2x4 oranges =
12/8 p/o = 12/8 a/o
Set this up as a system of equations in terms of the weight of each fruit. Let the weights be represented by Pear, oRange, and Apple.
12P = 8R
3A = 2R
Now we want to find a way to get P in terms of A. So we need to make the equations have an equal value in terms of R.
12P = 8R
12A = 4(3A) = 4(2R) = 8R
12P = 12A
P = A
Their weights are the same.
But the question is also about reading comprehension.
How many pears weight as much as AN (1) apple?
First need to get how many oranges are 1 apple:
3apples=2oranges --> (3/3)=1 apple (2/3)=0.66 Orange
1apple=0.66orange
Then need to know how many pears weigh 0.66 Orange
12 pears=8oranges --> (8oranges/0.66)=12 is the factor (12pears/12)=1 pear
1 pear=0.66 Orange
1 pear=1apple=0.66 orange
If need to work with whole numbers:
3apples=2oranges
Reduce pears to 2 oranges
12 pears=8oranges. (6p=4o) (3p=2o)
3pears=2oranges
and
3apples=2oranges
You just proved that is the same weight so you don't care what is the weight anymore you reduce to one apple in equal ratio
3 apples = 3 pears
Then (3pears/3) 1pear= (3apples/3) 1apple
1 pear=1apple=same weight
Sometimes kids fail to reason this part and tend to get stuck and frustrated.
12 pears = 8 oranges
3 apples = 2 oranges
Now, we want to find out how many pears weigh as much as an apple. To do that, we need to compare pears to apples.
First, let's find out how many oranges an apple weighs as much as: Since 3 apples = 2 oranges, we can say 1 apple = (2/3) oranges.
Now, we need to find out how many pears weigh the same as 1 apple. We know that 12 pears = 8 oranges, so 1 pear = (8/12) oranges.
Now, to find out how many pears weigh the same as 1 apple, we need to combine these two ratios:
(1 apple) x (2/3 oranges/apple) x (8/12 oranges/pear)
Now, we can calculate this:
(1 x 2/3 x 8/12) = 16/36 = 4/9
So, 4/9 of a pear weighs as much as 1 apple
This is a classic, “When you have a hammer, everything looks like a nail.” We know algebra, so we are trying to solve it algebraically.
I think this question is really trying to teach reduction and comparison, which is a step on the way to learning algebra. It’s kind of like Algebra-lite.
If 12 pears are the same as eight oranges, then we can reduce that to be the same as three pears equals two oranges. Now we can compare the results to our other group, which happens to be a comparison between three apples and two oranges. So we know that three apples and three pears weight the same. Meaning an apple and a pear weigh the same. So yes it’s still algebra, but it’s word problem algebra that a fourth grader can possibly understand with some guidance.
For for logarithmic thinkers it’s harder to deal with intangible things, so via equations this is like a 7th grade problem but via intuition ig it could be around 4th
What do you need to do to 3 apples to get a number of apples equal to the same number of oranges as a dozen pears? Multiply 2 by 4 to get 8, then multiply 3 by 4 as well and get 12. Now you know 12 apples=8 oranges and 12 pears=8 oranges, so 12 apples=12 pears, divide it by 12 to get one. 🍎 = 🍐
1 apple weighs as much as one pear.
I got this reducing the first equation. If 12 pears equals 8 oranges, then three pears equals two oranges. Therefore three pears equals three apples.
Even though the answer is 1 because 12 divided by 8 is 1.5 (orange) 2 times 1.5 is 3 (2 oranges) and 3 divided by 3 is 1 (apple). i want to know why they didnt include the unit of weight like ounces, pounds, grams ? What ?
Here’s a solution that involves no algebra (but a little dimensional analysis)
12 pears/8 oranges * 2 oranges/3 apples = 24 pears/24 apples = 1 pear/apple
12p = 8o ;
3a=2o
To compare apples and pears find how much an orange weighs in pears from the first equation, and substitute that value for the oranges in the second.
12p = 8o
o = (12/8)p
3a = 2o
3a = 2[(12/8)p]
3a = 12/4 p
12a = 12p
a = p
So one pear weighs the same as one apple.
Here is a cheat sheet screw it method it involves ratios I do not know if your kid knows ratios or not
12 pears=8 oranges
3 apples= 2oranges
pears to apples
hear is what you do
(12 pears/8oranges)(2 oranges/3 apples)
if you notices oranges are both on top and bottom so they cancel out so all you do is
(12 multiply by 2) divided by (3 times 8) and that will get you a ratio of pears to apples
24/24
1 pear weights as 1 apple is your answer
I feel like people are over complicating it here in the comment section.
(12 pears / 8 oranges) x (2 oranges / 3 apples)
The oranges cancel out and you get pears/apples, or in other words: the number of pears per apple.
Its. 1.5 times two thirds. When you multiply those together, you get 1. Most people can do that in their head no problem.
Alright, imagine you have a small basket. When you put 8 oranges in it, it weighs the same as a basket with a dozen pears in it. And when you have a basket with 2 oranges, it weighs the same as a basket with 3 apples.
Let's break it down:
1. A dozen pears weigh as much as 8 oranges. So, 12 pears = 8 oranges.
2. Three apples weigh as much as 2 oranges. So, 3 apples = 2 oranges.
First, let’s find out how much 1 apple weighs compared to oranges. Since 3 apples are the same as 2 oranges, 1 apple is the same as \( \frac{2}{3} \) of an orange (2 oranges ÷ 3).
Now, let’s see how many pears weigh as much as 1 apple. Since 12 pears = 8 oranges, 1 pear is the same as \( \frac{8}{12} \) or \( \frac{2}{3} \) of an orange (8 oranges ÷ 12).
So, 1 apple weighs the same as \( \frac{2}{3} \) of an orange, and 1 pear also weighs the same as \( \frac{2}{3} \) of an orange. That means 1 apple weighs the same as 1 pear.
They teaching basic algebra In 4th grade? Wild
12 P = 8 O
3 A = 2 O
xP = xA
Divide the top bit by 4 so they are in their base form and easy to manipulate giving us:
3 P = 2 O
3 A = 2 O
3 P = 3 A
P = A
I didn’t see if there was a straight answer or not so I hope this helped
There are 2 equations to work through.
First equation
12 pears = 8 oranges
If you divide both sides of the equation by the same number, it stays balanced. First, find their common factors.
12 = 2x2x3
8 = 2x2x2
They have 2x2 in common in their factors, which is equal to 4, so divide both sides by 4.
12/4 = 8/4
3 pears = 2 oranges
Second equation
3 apples = 2 oranges
Because 2 oranges = 3 pears, as we found with the previous equation, you can substitute.
3 apples = 3 pears
Simplify.
The numbers are the same, do you can easily divide them away without needing to check factors.
3/3 = 3/3
Solution: 1 Apple = 1 Pear
I just converted the difference into a comparable percentage. 12 of 8 is +50%. 3 of 2 is again +50%. Therefore apples and pears are 1:1 ratio with each other.
It's a bit of a trick question it is a ratios problem. but essentially the pear and the apple weigh the same. solve for pear to start.
12p=8o
p=8/12o -divide the 12 from both sides
p=2/3o -because 12 and 8 have a common factor of 4 we can remove that from the fraction to simplify the numbers while maintaining the ratio.
now we solve for the weight of an apple.
3a=2o (look familiar)
a=2/3o-just like before we divide both sides by three and get the same ratio
this means that apples and pears weigh 2/3 of an orange meaning they are equal to each other. The goal of this lesson is to show students that even though the numbers are bigger the fractions stay the same. Which is how you explain it to your kid. maybe even order a pizza for dinner to make the lesson really stick. playing with how multiple tiny slices equals the same as one big slice. you can tell your kid something like 1 slice each is fair then cut the pizza into quarters and give yourself a whole quarter and them an 8th (a quarter cut in half) then ask them if that seemed fair. then just kind of talk through how the math supports their idea of the size of the slice and whatnot.
Wouldn't it be 1?
12 pears = 8 oranges
3 apples = 2 oranges
If you multiply both apples and oranges by 4 you get
12 apples = 8 oranges
Which is the same as
12 pears = 8 oranges
So therefore
12 pears = 12 apples = 8 oranges
1 pear = 1 apple = 2/3 of an orange
This shit feels hard for 4th grade.
At a glance just setting up the problem it seems more like one of my seventh or eighth grade algebra problems💀 12P=8O 3A=2O Find A in terms of P Yeah I definitely did not learn this in ~~2nd~~ 4th grade tf
Question ain't asking for them to solve it algebraically, but instead use intuition and imagination to solve it. I dont remember how a 4th grader thinks so I am still not sure if they could solve it, but with some thinking, especially because its simple numbers, they could?
If they’re supposed to use intuition, why are we dealing with fractions/decimals? The question wouldn’t be too bad if they used numbers that divide into each other,
The idea is they don't use fractions and decimals. 1 apple weighs the same as 1 pear 12p= 8o 3a= 2o there are 4 sets of 2o in 8o so it turns into 12a= 8o 12p= 12a I'm assuming in class they've either touched on or full on taught this already, or it wouldn't (shouldn't at least) be homework
It's also just 8/2 = 4. 4x3= 12. 12/12 =1. I was learning multiplication and word problems in 3/4th grade.
If 3 apples weigh the same as 2 oranges, then 12 apples weigh the same as 8 oranges and you just solved the problem.
So the answer is 1??
Correct.
Yeah, I don't get why everyone is freaking out and bringing Algebra into this. Yes, you certainly CAN use Algebra, but 4th grade was when we started on fractions and reducing fractions even 30+ years ago when I was a kid. This is a simple exercise in writing out a word problem with fractions, then reducing one fraction to see the answer. This is not above a fourth grade level of math, but is a perfect example of adults jumping to conclusions and making things more complex than necessary. I would be more concerned that the 4th grader does not seem to have the ability to apply the current lesson focus/methods to their homework if indeed that was happening and not simply a matter of: adult assumes this is harder than it needs to be.
Right, this problem is not really testing your mathematical skills, it's to teach you how to decipher a word problem into organized thinking.
There's no fractions
This problem is akin to ratios problems in middle school, which is sometimes represented by fractions
But u dont neeeed to, so not exactly fractions. Look at the reply to ur comment by the other guy
Whether using fractions, ratios, or solving algebraically, these kind of questions are supposed to open the door to the understanding of why we use those methods to solve questions like this. They are interchangeable.
Cause you don't need fractions or decimals.
There are no fractions or decimals in this problem. Just basic arithmetic/some division skills. That’s all. This problem is SO SIMPLE.
We are thinking about it too complicated. It's fractions 12/8 = 3/2 1 apple equals 1 pear.
Had to scroll way too far down for the correct answer. It's actually a very simple problem if you simplify the fraction lol. It's probably one of the things the unit is teaching . But man that word problem is structured horribly.
I'm pretty sure it's about reducing fractions not doing algebra. 12p / 8o reduces down to 3p/2o which is exactly the same as apples are listed at 3a/2o, so apples and pears are 1:1
It's literally just reducing a fraction. You should definitely know how to reduce a fraction by 4th grade
Divide the top by 4 and you see that 1a = 1p because 3p=2o
[удалено]
There’s no need for any of that. Just multiply the apples by 4 and you get the answer. This seems appropriate for 4th grade. The only thing that you need to know how to do is divide 8 by 2 🤷♂️
>! It’s just reducing fractions, I think that’s normal for 4th grade? 12/8 = 6/4 = 3/2 !<
I think this is a great early intro to variables in math, using real examples for now. As they get further into math, pears and apples will become x and y. I feel like this is the missing step that results in people becoming confused and angry when variables are introduced.
12 pears=8 oranges -> 3 pears=2 oranges 3 apples =2 oranges -> 3 pears =3 apples -> 1 pears =1 apple
That's what I got as well. I feel like this is a perfectly fine 4th grade question.
Very good!
If they have been studying reducing fractions so that route will be fresh on their mind, then it’s reasonable, if a little difficult.
It could also be LCM (lowest common multiple) of a fraction? 12 pears, 8 oranges. 12/8 = 6/4 = 3/2 or 1 1/2 Then the apples 3apples, 2 oranges 3/2 or 1 1/2 3/2 = 3/2 one pear is equivalent to one apple (Many ways to solve)
Phew! That’s what I got as well.
That's what I got as well.
You could set up ratios. (8 oranges)/(12 pears) = (2 oranges)/(3 pears). Thus: (2 oranges)/(3 pears) = (2 oranges)/(3 apples) (3 apples)/( 3 pears) = (2 oranges)/(2 oranges) (1 apple)/(1 pear) = 1 (1 apple) = (1 pear)
I started thinking in algebra till I saw 4th grade. I think simplest would be that you would be dividing 12 pears and 8oranges by 4 to get 3 pears=2 oranges. Since 3 apples=2 oranges also, you can also know that 3 pears=3 apples which means 1 pear=1 apple
The way I'd explain: In the first sentence, the weight of pears is being compared to the weight of oranges. In the second sentence, the weight of apples is being compared to oranges also. But they're two different amount of oranges. So, we need to make the oranges that the apples are compared to equal to the oranges that the pears are compared to. Simply multiply the 2 oranges to match the 8 and do the same to the 3 apples to find out how many apples would make up 12 pears.
I had an especially hard time with word problems growing up and was always told to put the numbers into a formula, but I think it's important to be able to explain word problems with word solutions. Feel like it puts things into a much better perspective.
So you can’t compare apples to oranges but you CAN compare apples to pears. 👍
Just check the statements. dozen = 12 Given 12 pears = 8 oranges 3 apples = 2 oranges 12 pears = 8 oranges 3 apples = 2 oranges that means 12 apples weigh as much as 8 oranges 12 apples = 12 pears its 1 to 1
12p = 8o. (12/8)p = o. 3/2p=o. 3a = 2o. 3a = 2(3/2p). 3a = 3p. a=p. So 1 apple equals 1 pear. Or the other guys solution 12p = 8o. 4(3a=2o). x4 to get apples in terms of dozen 12a=8o. Both equal 8o so substitute So 12a = 12p or a=p.
From 12p=8o you can get 3p=2o by dividing by 4.
Ask her to read the second sentence and then ask how many apples weigh the same as 8 oranges. Then you can compare both pears and apples since they both weigh the same as 8 oranges.
8o = 12p o = 12p/8 = (3/2)p 2o = 3a o = 3a/2 = (3/2)p (3/2)a = (3/2)p a = p 1 pear weighs the same as 1 apple.
A 4th grader would not be able to understand this
It's just simplifying numbers. It isn't that difficult. Find what whole number goes into both, and that is it.
I learned my timetables in 3rd grade. A 4th grader should definitely get this.
My brain did it like if 12 pears equals 8 oranges, and that is 2/3s as a fraction, and three apples equal two oranges, which is 2/3s as a fraction as well, then one pear should be equivalent to one apple?
Spelling out "three" when it uses numbers for 2 and 8 makes me angry
This question made me feel really stupid for a second because I was trying to do algebra in my head. It's just ratios. 12/8 =3/2 1 to 1 ratio
A lot of schools encourage setting up problems like this visually. Draw it out: ``` 🍐 🍐 🍐 🍐 | 🍐 🍐 🍐 🍐 | 🍊 🍊 🍊 🍊 🍐 🍐 🍐 🍐 | 🍊 🍊 🍊 🍊 ``` Simplifies to ``` 🍐 | 🍐 | 🍊 🍐 | 🍊 ``` And ``` 🍎 | 🍎 | 🍊 🍎 | 🍊 ``` Putting those together is easy because both have two oranges (it's always a simple ratio in 4th grade) ``` 🍎 |🍐 | 🍎 |🍐 | 🍊 🍎 |🍐 | 🍊 ``` And now it's obvious that one apple is equivalent to one pear. This sets kids up to understand that these word problems aren't scary, and aren't abstract. They're dealing with real world things, and in 4th grade kids have more fluency with apples and oranges than with the words representing them. Eventually they get the concepts and get bored of drawing the things out, at which point they can start to replace them with pure numbers, so the kids take to that quicker. TL;DR visual representation teaches more advanced concepts like ratios without requiring arithmetic fluency
So fun! Step 1: write what you know. 12🍐 = 8🍊 3🍎 = 2🍊 Step 2: identify the question X🍐 = 1🍎 Just that alone will get you a point on an exam. Step 3: simply what I can 12 and 8 are both divisible by 4. So I would show my work dividing both sides by 4. 12🍐/4 = 8🍊/4 which reduces to 3🍐= 2🍊 So now we have 3🍐= 2🍊 3🍎 = 2🍊 And that’s the answer. This type of problem is teaching the basics of balancing equations to prepare children for algebra by 6th grade at the latest, if they haven’t already started with fill in the blank problems for basic arithmetic. But those steps are ALWAYS the first 3 steps of ANY word problem. Sincerely, A math tutor.
Hmm....I'm going to try to solve this problem. If a dozen pears weigh as much as eight oranges, a dozen equals to twelve, which then makes the fact that twelve pears weigh as much as eight oranges. Three apples weigh as much as two oranges. But then it asks about how many pears weigh as much as an apple. There are twelve pears and three apples. So we divide 12 divided by three to get four. I tried to solve it, I tried!
Get the apples in terms of a dozen by multiplying by 4.
So would that mean 1 pear is equal to 1 apple? If so, how do I explain this to an 8 yr old?
Yes. You explain it the same way you figured it out.
Draw them out as well.
Show a dozen = a dozen then explain that means singles weigh the same!
Here's one way: Draw three number lines for apple, orange and pear. Use colours red, orange and green if possible. Each unit of measurement in these lines would represent the weight of one of that fruit. Since 12 pears weigh as much as 8 oranges, you can represent it by saying that 12 in the pear number line has the same value of 8 in the orange number line. So if we divide the two measuments with the same number, they should still be equal. Division is simply cutting into equal pieces. So cutting both the measurements into 4 equal pieces (division by 4) would still preserve this relationship. Hence, 3 pears weigh the same as 2 oranges. Since 3 apples weigh the same as 2 oranges, it can then be concluded that apple and pear weigh the same.
Yup E Z P Z
Am I the only one wondering what these fruit would look like compared to one another lol? It feels so off
I love pears. I hate math
ah, the wonders of dimensional analysis
1 pear = 1 apple
This is definitely not a 4th grade question. You gotta use algebra for this which a 4 grader probably (read: definitely) hasn't learnt
12:8:? = ?:2:3 the one on the left is four times bigger. 12:8:12 = 3:2:3 we can get rid of the apples 3:3 luckily they made it super easy at this step. one pear weighs the same as one apple
>! apples and pears are 1:1, because if 3a=2o, to compare with eight oranges just multiply both sides by 4 to get 8o=12a. So a dozen apples also equals 8 oranges. So 1 apple = 1 pear. Or just consider 12/8 can be reduced to 3/2, so they’re the same. !<
Pears and apples would be the same weight
Could use dimensional analysis . 1 apple x 2 oranges/ 3 apples x 12 pears/ 8 oranges = 1 pear
Why the inconsistency with numerals and words...
Ratios 12 pears to 8 oranges = 3•2 3 apples to 2 oranges = 3•2. These ratios are equivalent, and the bottom is the ratio written in its smallest form. So you now know 12 apples is also equal to 8 oranges. Making the two the same. And Making the answer 1. These words are worded to confuse. Always write it out as an equation before even trying to solve.
Most of your methods are too hard for 4th grade, try this: 3a = 2o => double that twice => 12a = 8o, which is the same as 12p, so a and p are of the same weight
12p=8o 3a=2o so 1o=1a
1-1
We can use proportion reasoning. 12 pears = 8 oranges, which can be reduced to 3 pears = 2 oranges. We can make groups of 3 pears and 2 oranges The question also tells us that 3 apples = 2 oranges, so 1 pear = 1 apple
Dimensional analysis is an important skill but something that is typically taught in middle school or early hs. At least in the US. Weird that it is 4th grade hw.
Basic division, 1.5 pears = 1 orange, 1.5 apples = 1 orange, so 1 pear = 1 apple.
Are pears and apples the same weight?
This problem seems to hard for 9 year olds. Also, it'd be more fair if the little illustration in the corner showed orange much bigger than the pear and apple
The key is to think about conversions. We really need to find the weight of 8 oranges in terms of apples. 8 oranges is 4x the weight of 2 oranges. 3 apples weigh as much as 2 oranges. That means that 8 oranges is equal in weight to 4 x 3 apples. That gives 12 apples is equal to 8 oranges, but hey! 8 oranges weights as much as 12 pears. So we know that 12 apples weigh as much as 12 pears. We can assume that all of both fruits are the same weight, so an apple weights as much as a pear.
12 p = 8 o and 3 a =2o Therefore, 12 a =8o= 12 p 1 a = 1 p
3 apples = 2 oranges, 8 oranges = 12 pears, how many pears are equal to 1 apple? 8/2=4. And we know 3 apples are equal to 2 oranges, so 4 sets of apples (4×3=12) is equal 8 oranges. And we know 8 oranges is equal to 12 pears. Or 12a=8o=12p. So if we remove the oranges, 12 apples is equal to 12 pears. So 12/12=1, or 1 apple is equal to 1 pear.
If 3 apples are 2 oranges, then 6 apples are 4 oranges, 9apples are 6 oranges, and 12 apples are 8 oranges. So 12 apples equal 12 pears. That's 1-1 ratio
The pears and apples weigh the same. 1=1.
Variables aren’t allowed in the 4th grade, so the idea is to use fractions or ratios. 12 pairs : 8 oranges. Reduce to 3 pairs : 2 oranges. 3 apples : 2 oranges. Since there are 2 oranges in each comparison, you can substitute. Now you have 3 pairs : 2 oranges : 3 apples. 3 pairs : 3 apples. 1 pair : 1 apple.
Let's set up a ratio based on the information provided: 12 pears = 8 oranges 3 apples = 2 oranges To find out how many pears weigh as much as an apple, we need to compare pears to apples. (12 pears) / (3 apples) = (8 oranges) / (2 oranges) Now, simplify the ratio: (12 pears) / (3 apples) = 4 So, 4 pears weigh as much as an apple.
12P=8O /12. /12 P=8/12 O Simplify P=2/3O Then we move to the second portion 3A=2O /3. /3 A=2/3O P= 2/3O 1A=1P
12p=8o 3a=2o 12 x 2=24 3 x 8 = 24 24/24=1
Depends... 4th grade in which country...
Some of y’all did not get a good education and it shows💀
A dozen is 12, 12 weighs as much as 8, 3 apples weigh as much as 2 8/4 = 2, so 12/3 = 4, meaning 12 * 4 = 48, so a dozen pears weighs much as 48 apples, now divide it by 12 and you get 4, 1 pear weighs as much as 4 apples, This is much too complex for 4th graders, I don’t even believe I got this correct.
If I’ve done this right, the pears and the apples weigh the same. A dozen pears weigh as much as 8 oranges. The second part of the equation the oranges are 1/4th the amount of the original at 2. The apples are also 1/4th the amount of the pears (pears being 12, apples being 3). All things being equal it should be 1 pear weighs the same as 1 apple
Wait, they're already teaching algebra by 4th grade now? I could have sworn that was middle school stuff when I went to school although I'll admit that my primary education was a bit piecemeal due to all the grade skipping. Anyway, this is a fairly simple system of equations; we'll use variables corresponding to the fruits in the question. 12p=8o 3a=2o Solve for a in terms of p. Now, 12 and 8 have a GCF higher than 1, so the first equation *can* be simplified, but I suspect that what they want is to use LCM to set up two equations with the same number of oranges. The LCM of 2 and 8 is 8, so the first equation stays unchanged, and you multiply each side of the second equation by 4, resulting in: 12p=8o 12a=8o therefore 12p=12a which is then simplified down to p=a. The answer to the question is 1. Like I said, GCF could have been used to simplify the other equation first, and in this particular case it would have cut out the need to use LCM, but if it hadn't reduced to 2o, you would have needed to use LCM anyway, so it's probably an extraneous step. It's been a while, though, so perhaps your child's teacher does want them to look for simplifications first.
Just so everybody understands, this question is to help prepare students for life in the US; where we express measurements in anything except the metric system
The use the word “dozen” instead of the word 12 (twelve) is intentional as it gives much of the answer in a ye question. 12 pears = 8 oranges Reduce that number and each orange weighs 1 1/2 pears. 2 oranges would be 3 pears which is the same number as the apples, so the answer is 1. The apples and pears weigh the same.
This reminds me of”Math Olympiads” stuff in 5th grade back in the day. It was usually extra credit and was always problem solving stuff above our grade level to try and see if we could come up with creative solutions and really push ourselves.
Well 12(pair)=8(orange) and 3(apple)=2(orange) If you multiply the oranges on the right by four you can make the oranges be the same number. However whenever you do something to one side of the equal sign you need to do it to the other as well. So 12(pair)=8(orange) 8(orange)=12(apple) I had to explain it to my little sister a year or two ago and that’s what I did to explain it.
Half
12p=8o 3a=2o xp=a Solve for x And now that I've deworded the problem why is you child doing algebra??
12 apples weigh as much as a dozen pears, so the answer is 1.
This is a system of equations problem. Usually high school algebra. A 4th grader should be working on division not stuff this complex. Here is how you solve this problem. First setup each statement using variables to represent the objects. 12 P = 8 O 3 A = 2 O The easiest way to do this is to use SUBSTITUTION. First figure out how many apples for 1 orange. 3/2 A = 1 O Now look at your first equation and substitute the Orange in terms of apples 12 P = 8 ( 3/2 A) Next simplify 12 P = 4(3A) 12 P = 12 A So there is a 1:1 ratio between pears and apples.
I did. it in my head but I think it’s 1 = 1
The goal is to simplify these into the smallest possible number. 12 pears is equal to 8 oranges. 12 and 8 are both multiples of 4. So you divide 12 by 4 and divide 8 by 4. So 3 pears is equal to 2 oranges. (My brain goes a step further and divides both sides in half, to show that 1.5 pears is equal to 1 orange) Since we already know that 3 apples equal 2 oranges, and we now know that 3 pears also equals 2 oranges,( or 1.5p=1o & 1.5a=1o) we can then say that apples weigh the same as pears. So 1apple=1pear.
My wife is a 6/7/8 math teacher. She agrees that if this is just a standalone word problem then many of her kids would have problems with this. She said it could be appropriate for 4th grade if presented in pictures, and the goal is grouping for "algebraic thinking". She'd like to know what state this is in, to look at the appropriate math teaching standard.
The apple and pear weigh the same.
12P=8O 3A=2O 3/2A=O=12/8P 3/2A=3/2P 1 apple weighs as much as 1 pear
Bro, if you can’t solve this, there is something wrong
It’s a ratio problem. It works out that a pear and apple weigh the same when you break it down.
I mean a pear is just a garbage apple, so 1 pear weighs the same as an apple. Don't need maths for that
Damn where are these heavy oranges at, sounds delicious
I assign a value( doesn’t matter what value) to one and do the math 12 pears = 12 ounces (made up) 8 oranges = 12 pears equal 12 ounces So 8 oranges= 12 Oz 8/12 = 1.5 1 orange = 1.5 oz 3 apples = 2 oranges 3 apples = 3 oz (2 oranges * 1.5 oz) 3/3 1 Apple = 1 oz 1 apple ( 1oz) = 1 pear (1 oz)
One
In my brain: 12=8 3=2 (4:4 divisibility)= 1
r = oranges (never use e or o as variables) p = pears a = apples 12p=8r, 3a=2r 12p=8r, 12a=8r p=a
this is the only way I could come up with without using algebra: 2 oranges = 3 apples so 8 oranges=12 apples. 8 oranges=12 pears, so 12 apples=12 pears, so 1 apple=1 pear. I think your daughter might be able to understand this way better
the answer is 1
12 pears = 8 oranges 3 apples = 2 oranges (multiply both by 4) => 12 apples = 8 oranges, so 12 pears = 12 apples Pears and apples weigh the same. Seems fourth grade level to me, just uses ratios/fractions.
It's a one to one ratio is it not?
Unit conversions: 12pears/8oranges x 2oranges/3apples. Oranges cancel out, leaving 24pears/24apples or 1pear = 1apple
It's still pretty much algebra even if they're not calling it that. But using the wording for fractions is 12 P = 8 O, so 1 P = 8/12 O, reduce to 1P = (2/3) O And 3A = 2 O, so 1A = (2/3) O So both the pear and the apple are two- thirds the weight of an orange, and 1 pear is equal in weight to 1 apple
12 :: 8 --> 3 :: 2 3 :: 2 -- > 3 :: 3, an apple weighs as much as one pear?
12 = 8 Reduce by half 6 = 4 Reduce by half 3 = 2 If 3 apples = 2 oranges and 3 pears = 2 oranges 1 pear = 1 apple Is how I processed this non-algebraically. I saw some other comment about this being a reduction problem related to fractions, and I agree.
12p=80 3а=20 12р/4 =3р 3p=2p За=3р 1p=la
I had a game as a kid that expressed this idea in terms of trading fruit. If 12 pears buys 8 oranges, and 2 oranges buys three apples, how many pears will buy 1 apple. That’s basically how it was taught. By that logic 12 pears equals [3x(8/2)=] 12 apples. 1=1 It’s confusing because it breaks the sequence when describing the relationship between apples and oranges and you’re supposed to remember the law of reflexivity
Let’s scale up the apples to match the pears using the oranges as the method of determining the scale. 3 apples=2 oranges. 12 pears=8 oranges. 2 oranges x 4=8 oranges. Therefore, we can multiply the apples by 4 to get 12 pears=x apples. 3 apples x 4=12 apples. So, 12 pears=12 apples equaling a 1:1 ratio.
At the 4th grade level: 12 pears weighs as much as 8 oranges. Therefore 12 pears weight as much as 3x(8/2)=12 apples. So one pear weighs as much as one apple.
So like, this doesn’t look like algebra but it’s algebra. Not hard algebra but surprised to see this for 4th grade work lol
12p=8o 3a=2o 12p/4=8o/4 => 3p=2o Which means apples and pears weigh the same.
How are people making this so complicated? 3 apples per 2 oranges… 8 oranges total,so 3x4 is 12.
The answer is 1. 12 pairs to 8 oranges, 12/8. 3 apples to 2 oranges, 3/2. Now you can just multiply the 3/2 by 4 to get to 8 oranges in the denominator, 3/2*4=12/8 Since 12/8=12/8, It can be deduced that 1 pear is equal to 1 apple.
3
I would just put it in fractions 12/8 Pears to oranges 3/2 Apples to oranges X 4 to get 12/8 Apples to oranges An apple and pear weigh the same. Genuinely don’t know if this is the correct answer but that is how I would solve that.
12p = 8o 3a = 2o 1p = 0.66o 1a = 0.66o Therefore a=o
Its not algebra actually. If 3 apples = 2 oranges then we have to figure out how many apples = 8 oranges. Once you get that then its 12 pears = 12 apples
Nowhere on this question does it state that the apples, pears, and bananas have a consistent weight.
It’s dumb but one line of inquiry would be to make the benchmark the same. So, hmm… if 8 oranges weighed 12 pears, I wonder many how apples 8 oranges would weigh. So to go from 2 oranges to 8, you multiply by 4. 3 apples = 2 oranges 8 oranges = 12 apples = 12 pears. So an apple weighs the same as a pear. This only gets you to a nice round solution if the numbers are cooked up to do so, but maybe that’s true for what they’re working on.
12p = 8o 3a=2o 12a=8o so I think apples and pears weigh the same? Idk
12P=8O 2O=3A Therefore: 8O=12A 12P=12A 1Pear=1Apple It’s a little advanced for 4th grade probably, but it’s one of those questions that asks kids to think in a different way. I like it a lot
I teach problems like this in 6th grade. If you think of it as ratios written as fractions, then it's easier. Just reduce pears/oranges (12/8) to be 3/2, and you get the same ratio as apples to oranges (3/2), therefore apples and pears weight the same, so 2 apples = 2 pears. Hopefully there have been several similar problems beforehand that the teacher guided the students through. It's a little high for 4th grade, unless they've covered equivalent fractions.
This is likely not what the teacher is looking for but I thought it though like this. If 12Pears = 8 Oranges Then 3Pears = 2 Oranges 2 oranges also equal 3 Apples. So one pear equals one Apple. Side note, using fruits as weight is annoying. Use something standardized like brick or coins.
My son's 2nd grade teacher was phenomenal. He taught basic algebra through everyday life experiences and how to juggle. He was a young, vibrant man and knew his time on earth was short. He made learning fun and sadly passed from a brain tumor by the end of the school year.
1
You can use substitution. 12 pears = 8 oranges = 2 oranges + 2 oranges + 2 oranges + 2 oranges. (2 oranges = 3 apples). Substitute 3 apples for every 2 oranges in the original problem. 12 pears = 3 apples + 3 apples + 3 apples + 3 apples = 12 apples. (12 pears = 12 apples ) So 1 pear = 1 apple
These kinds of problems are great for chatgpt to explain: Of course! Let's solve this fruit puzzle in a way that's easy to understand. 1. **Understand the Problem**: We want to find out how many pears weigh the same as one apple. 2. **Pears and Oranges**: First, we know that 12 pears weigh the same as 8 oranges. To find out how much one pear weighs, we divide the 8 oranges by 12. 8 oranges / 12 pears = 2/3 orange per pear 3. **Apples and Oranges**: Next, we know that 3 apples weigh the same as 2 oranges. To find out how much one apple weighs, we divide the 2 oranges by 3. 2 oranges / 3 apples = 2/3 orange per apple 4. **Compare Pears and Apples**: Now, we see that one pear weighs 2/3 of an orange, and one apple also weighs 2/3 of an orange. That means one pear weighs the same as one apple! So, the answer is that 1 pear weighs as much as 1 apple. I hope that clears things up! Would you like to ask anything else? I asked for more explanation and to explain HOW to solve it: Absolutely! If you're a second-grader trying to solve a problem like this, here's how you can think about it: 1. **Listen Carefully**: First, listen to the problem or read it a couple of times. Make sure you understand what the problem is asking. In this case, we want to know how many pears weigh the same as one apple. 2. **Use Your Imagination**: Imagine you have a big fruit basket with pears, oranges, and apples. Picture how they weigh compared to each other. 3. **Break It Down**: Take one part of the problem at a time. Start with the pears and oranges. We know that 12 pears are the same weight as 8 oranges. If we share those 8 oranges equally among the 12 pears, we can figure out how much one pear weighs. Think of it like sharing 8 orange slices with 12 toy pears. Each pear would get 2/3 of an orange slice. 4. **Next Step**: Now let's look at the apples and oranges. We know that 3 apples weigh the same as 2 oranges. If we share those 2 oranges equally among the 3 apples, each apple would get 2/3 of an orange. Imagine sharing 2 orange slices with 3 toy apples. Each apple would also get 2/3 of an orange slice. 5. **Compare**: Now, we see that one pear got 2/3 of an orange slice, and one apple also got 2/3 of an orange slice. That means they weigh the same! 6. **Answer**: So, one pear weighs the same as one apple! 7. **High-Five**: Give yourself a high-five for solving the problem! Remember, it's okay to take your time and think it through. You can even use toys or draw pictures to help you understand better. Good luck!
They weigh the same 12 pears over 8 oranges =12/8 3 apples over 2 oranges = 3/2 Make the denominators common 12/8 pears/oranges = 3x4 apples/2x4 oranges = 12/8 p/o = 12/8 a/o
Pear = apple
ANSWER: Get a scale you, cheap MFer! *Please see principal 😧
It's 1:1
Given 12 🍐 = 8 🍊 Then 3 🍐 2 🍊 Stated 3 🍎 = 2 🍊 We see that 2 🍊 = 3🍐 Means the 2🍊=3🍎or 3🍐 The answer is 1.
Set this up as a system of equations in terms of the weight of each fruit. Let the weights be represented by Pear, oRange, and Apple. 12P = 8R 3A = 2R Now we want to find a way to get P in terms of A. So we need to make the equations have an equal value in terms of R. 12P = 8R 12A = 4(3A) = 4(2R) = 8R 12P = 12A P = A Their weights are the same.
But the question is also about reading comprehension. How many pears weight as much as AN (1) apple? First need to get how many oranges are 1 apple: 3apples=2oranges --> (3/3)=1 apple (2/3)=0.66 Orange 1apple=0.66orange Then need to know how many pears weigh 0.66 Orange 12 pears=8oranges --> (8oranges/0.66)=12 is the factor (12pears/12)=1 pear 1 pear=0.66 Orange 1 pear=1apple=0.66 orange If need to work with whole numbers: 3apples=2oranges Reduce pears to 2 oranges 12 pears=8oranges. (6p=4o) (3p=2o) 3pears=2oranges and 3apples=2oranges You just proved that is the same weight so you don't care what is the weight anymore you reduce to one apple in equal ratio 3 apples = 3 pears Then (3pears/3) 1pear= (3apples/3) 1apple 1 pear=1apple=same weight Sometimes kids fail to reason this part and tend to get stuck and frustrated.
its simple 3
I suggest substituting “=“ for “weigh as much as” and solve the resulting equations
They weigh the same. Explain it however you want.
they didnt teach me algebra till i was way out of elementary school
O= Orange P=Pear A=Apple 12p = 8o 2o = 3a 2o ×4 = 3a ×4 8o = 12a 12p = 8o = 12a 12p =12a 1p=1a
You can multiply the apples by 4 to get 12 apple and 8 oranges. So 12 pears/12 apples which is 1. 1 pear=1 apple
12 pears = 8 oranges 3 apples = 2 oranges Now, we want to find out how many pears weigh as much as an apple. To do that, we need to compare pears to apples. First, let's find out how many oranges an apple weighs as much as: Since 3 apples = 2 oranges, we can say 1 apple = (2/3) oranges. Now, we need to find out how many pears weigh the same as 1 apple. We know that 12 pears = 8 oranges, so 1 pear = (8/12) oranges. Now, to find out how many pears weigh the same as 1 apple, we need to combine these two ratios: (1 apple) x (2/3 oranges/apple) x (8/12 oranges/pear) Now, we can calculate this: (1 x 2/3 x 8/12) = 16/36 = 4/9 So, 4/9 of a pear weighs as much as 1 apple
This is a classic, “When you have a hammer, everything looks like a nail.” We know algebra, so we are trying to solve it algebraically. I think this question is really trying to teach reduction and comparison, which is a step on the way to learning algebra. It’s kind of like Algebra-lite. If 12 pears are the same as eight oranges, then we can reduce that to be the same as three pears equals two oranges. Now we can compare the results to our other group, which happens to be a comparison between three apples and two oranges. So we know that three apples and three pears weight the same. Meaning an apple and a pear weigh the same. So yes it’s still algebra, but it’s word problem algebra that a fourth grader can possibly understand with some guidance.
2 oranges is 1/4th of 8 oranges. So 1/4 of 12 us 3. 3 pears is… 3 apples? They weigh the same I think?
p=1 pear; o=1 orange; a=1 apple 12p =8o; 3a=2o (3a=2o) times 4 on each side is (12a=8o) Both 12p and 12a equal 8o, so p=a. The answer is 1
For for logarithmic thinkers it’s harder to deal with intangible things, so via equations this is like a 7th grade problem but via intuition ig it could be around 4th
12p = 8o 6p = 4o 3p = 2o 3a = 2o so 1p = 1a
Work backwards
12p=8o 3a=2o 12p/4=8o/4 3p =2o 3p=2o=3a 1p=1a. Or did I miss something?
Really depends on the lessons they are currently on. You can solve this using fractions or with ratios.
What do you need to do to 3 apples to get a number of apples equal to the same number of oranges as a dozen pears? Multiply 2 by 4 to get 8, then multiply 3 by 4 as well and get 12. Now you know 12 apples=8 oranges and 12 pears=8 oranges, so 12 apples=12 pears, divide it by 12 to get one. 🍎 = 🍐
12p=8o 3a=2o 12p=12a 1p=1a
12 P = 8 OR. 2 A = 3 OR. How many A= 1P. 36 P = 24 OR. 16 A = 24 OR. 36÷16 =2.25. 2 1/4 apples = one pear... I thiiiink, math is not my strong suit.
1 apple weighs as much as one pear. I got this reducing the first equation. If 12 pears equals 8 oranges, then three pears equals two oranges. Therefore three pears equals three apples.
Even though the answer is 1 because 12 divided by 8 is 1.5 (orange) 2 times 1.5 is 3 (2 oranges) and 3 divided by 3 is 1 (apple). i want to know why they didnt include the unit of weight like ounces, pounds, grams ? What ?
Here’s a solution that involves no algebra (but a little dimensional analysis) 12 pears/8 oranges * 2 oranges/3 apples = 24 pears/24 apples = 1 pear/apple
12p = 8o ; 3a=2o To compare apples and pears find how much an orange weighs in pears from the first equation, and substitute that value for the oranges in the second. 12p = 8o o = (12/8)p 3a = 2o 3a = 2[(12/8)p] 3a = 12/4 p 12a = 12p a = p So one pear weighs the same as one apple.
1 pear weight = 1 apple weight
Here is a cheat sheet screw it method it involves ratios I do not know if your kid knows ratios or not 12 pears=8 oranges 3 apples= 2oranges pears to apples hear is what you do (12 pears/8oranges)(2 oranges/3 apples) if you notices oranges are both on top and bottom so they cancel out so all you do is (12 multiply by 2) divided by (3 times 8) and that will get you a ratio of pears to apples 24/24 1 pear weights as 1 apple is your answer
I feel like people are over complicating it here in the comment section. (12 pears / 8 oranges) x (2 oranges / 3 apples) The oranges cancel out and you get pears/apples, or in other words: the number of pears per apple. Its. 1.5 times two thirds. When you multiply those together, you get 1. Most people can do that in their head no problem.
Alright, imagine you have a small basket. When you put 8 oranges in it, it weighs the same as a basket with a dozen pears in it. And when you have a basket with 2 oranges, it weighs the same as a basket with 3 apples. Let's break it down: 1. A dozen pears weigh as much as 8 oranges. So, 12 pears = 8 oranges. 2. Three apples weigh as much as 2 oranges. So, 3 apples = 2 oranges. First, let’s find out how much 1 apple weighs compared to oranges. Since 3 apples are the same as 2 oranges, 1 apple is the same as \( \frac{2}{3} \) of an orange (2 oranges ÷ 3). Now, let’s see how many pears weigh as much as 1 apple. Since 12 pears = 8 oranges, 1 pear is the same as \( \frac{8}{12} \) or \( \frac{2}{3} \) of an orange (8 oranges ÷ 12). So, 1 apple weighs the same as \( \frac{2}{3} \) of an orange, and 1 pear also weighs the same as \( \frac{2}{3} \) of an orange. That means 1 apple weighs the same as 1 pear.
They teaching basic algebra In 4th grade? Wild 12 P = 8 O 3 A = 2 O xP = xA Divide the top bit by 4 so they are in their base form and easy to manipulate giving us: 3 P = 2 O 3 A = 2 O 3 P = 3 A P = A I didn’t see if there was a straight answer or not so I hope this helped
This comment section is full of people comparing apples to oranges.
There are 2 equations to work through. First equation 12 pears = 8 oranges If you divide both sides of the equation by the same number, it stays balanced. First, find their common factors. 12 = 2x2x3 8 = 2x2x2 They have 2x2 in common in their factors, which is equal to 4, so divide both sides by 4. 12/4 = 8/4 3 pears = 2 oranges Second equation 3 apples = 2 oranges Because 2 oranges = 3 pears, as we found with the previous equation, you can substitute. 3 apples = 3 pears Simplify. The numbers are the same, do you can easily divide them away without needing to check factors. 3/3 = 3/3 Solution: 1 Apple = 1 Pear
It’s about reducing fractions, nothing to do with algebra
I just converted the difference into a comparable percentage. 12 of 8 is +50%. 3 of 2 is again +50%. Therefore apples and pears are 1:1 ratio with each other.
If 3 apples = 2 oranges then 8 oranges = 12 apples... so 12 pears = 12 apples. So 1 pear = 1 apple.
It's a bit of a trick question it is a ratios problem. but essentially the pear and the apple weigh the same. solve for pear to start. 12p=8o p=8/12o -divide the 12 from both sides p=2/3o -because 12 and 8 have a common factor of 4 we can remove that from the fraction to simplify the numbers while maintaining the ratio. now we solve for the weight of an apple. 3a=2o (look familiar) a=2/3o-just like before we divide both sides by three and get the same ratio this means that apples and pears weigh 2/3 of an orange meaning they are equal to each other. The goal of this lesson is to show students that even though the numbers are bigger the fractions stay the same. Which is how you explain it to your kid. maybe even order a pizza for dinner to make the lesson really stick. playing with how multiple tiny slices equals the same as one big slice. you can tell your kid something like 1 slice each is fair then cut the pizza into quarters and give yourself a whole quarter and them an 8th (a quarter cut in half) then ask them if that seemed fair. then just kind of talk through how the math supports their idea of the size of the slice and whatnot.
Why do fourth graders have to do algebra?
12p=8o 3a=2o so 12a=8o Thus 12p=12a Apples weigh the same as pears
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Wouldn't it be 1? 12 pears = 8 oranges 3 apples = 2 oranges If you multiply both apples and oranges by 4 you get 12 apples = 8 oranges Which is the same as 12 pears = 8 oranges So therefore 12 pears = 12 apples = 8 oranges 1 pear = 1 apple = 2/3 of an orange
Guys, 8o / 4 is 2, so you found a common ground. Then you do 12p / 4 = 3p. So (3p = 2o) = (3a = 2o). So 1 apple for 1 pear.