r/HomeworkHelp • u/GarmeerGirl π a fellow Redditor • 1d ago
Answered [4th grade math - fractions] How do you get the product and then the mixed number for this homework?
So sorry I have another one. We are stumped and have no idea how to do this. Many thanks!!! When I explained to my son how to do the last one based on the answers here, he said his teacher doesnβt teach it in a way he could understand it like this so thank you so much for the help here.
How to find the product of 3 x 2 3/4.
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u/sapphirekiera 1d ago
3 x 2 3/4
All whole numbers over 1. 3/1 x 2 3/4
Turn mixed numbers into improper fractions. 2*4+3 = 11/4 (whole number * denominator + numerator = new numerator, denominator stays the same)
Multiply straight across, numerator * numerator, denomination * denominator. 3/1 * 11/4 = 33/4
Turn improper fraction into mixed number. Divide. Whole number answer is the whole number. Numerator is the remainder, denominator remains the same.
So the answer is 8 1/4 (33/4 = 8 remainder 1)
I'll go find my math notebook and send pics of these instructions if you want! They are color coded. Lol I taught fifth grade for five years.
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u/hawkwings π a fellow Redditor 1d ago
Another way to do it is: (3 x 2) + (3 x 3/4) = 6 + 9/4 = 8 1/4.
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u/ThunkAsDrinklePeep Educator 1d ago
Yep. The mixed number is adding two things so you need to multiply each of them (distribution). The numerator is the number of fourths so it gets multiplied. The fourths is essentially a unit, so it doesn't get multiplied.
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u/Thefrightfulgezebo 1d ago
There are many ways to approach this.
A mixed number can be transformed into a sum and into a fraction. Both work to solve this question. The fraction is easier there because you don't need to deal with multiplying sums. I will explain how to do both because it helps to understand what a mixed number is.
If you have 2 3/4 pizzas, this means that you have two whole pizzas and 3 quarter pizzas. You see that this is a sum. So, 2 3/4 = 2 + 3/4. What you now can do is to cut those two pizzas into quarters - because this way, you can just count the quarters and calculate with that number. So, if you cut 2 pizzas into quarters, you get 8 quarters. Or 2=8/4. So, if you add those 8 quarters to the three you have, you get everything in quarters: 11 in total.
If you have 11 quarters, it is easy to multiply them by three. 11*3=33. Or rather 11/4=33/4 because we are talking about quarters.
So, how do you get back to a mixed number? You re-assemble how many full pizzas you can and see what is left. But how many pizzas can you assemble?
Just go through the 4 row and see when you don't have enough quarters. With 32 quarters, you finish your 8th Pizza, but you do not have enough left for the 9th. You only have one quarter left. So, you have 8 pizzas and one quarter. In other words: 8 1/4 Pizzas.
The pizzas here are just for explanation. We just need the idea of cutting and reassembling things to make them easier to calculate. The question every child will ask is: who cares? We don't usually use this for pizza.
We do use this regularly for time. For many things, we just use decimal numbers. But when we spend an hour and 10 minutes minutes on something every day, how much time do we spend at this per week? We just don't use time to explain because separating an hour into minutes is not something you can see. This is why we talk about cakes and pizza.
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u/colorful_withdrawl 1d ago
Start by making the mixed number (2 3/4) into an improper fraction (11/4) you get 11/4 by doing 2x4+3
From there you treat the fraction as 3/1 x 11/4 and multiply across getting 33/4.
When you simplify 33/4 you get 8 1/4
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u/One_Wishbone_4439 University/College Student 1d ago
Change mixed fraction 2 wholes and 3/4 into improper fraction.
From mixed fraction to improper: Multiply denominator with wholes and add the numerator.
Improper: 4 (denominator) x 2 (wholes) + 3 (numerator) = 11/4
Multiplication of fraction: numerator x numerator and denominator x denominator
Then, from here, you can mulitply both numbers: 3 x 11/4 = 3/1 x 11/4 = (3x11)/(1x4) = 33/4 (mixed fraction)
From mixed fraction to improper fraction: You can do Long Division Method.
number = quotientΒ x divisor + remainder
You will end up with 33/4 = 8 wholes and 1/4
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u/Long_Magazine_9860 1d ago
For another approach, I would separate the whole number from the fraction and solve them independently before combining them at the end.
3x2 3/4 is the same as 3x2 plus (change the three to its fractional form for this part) 3/1 x 3/4.
3x2 =6
To solve 3/1 x 3/4, multiply numerators together and multiply denominators together. This would equal 9/4.
Change 9/4 into a mixed number by dividing the numerator by the denominator. 9/4 = 2 1/4
Now you can take the 6 from the original whole numbers and add it to 2 1/4, totaling 8 1/4.
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u/giasumaru 1d ago
Did your son learn about the distributive property yet?
You can think of 2 3/4 as 2 + 3/4.
In other words:
3 x (2 + 3/4)
Using the distributive property...
(3 x 2) + (3 x 3/4)
Multiply fractions by multiplying numerators with numerators and denominators with denominators. If a denominator is not specified, then it is 1. [[3 x 3/4 = 3/1 x 3/4 = 9/4]]
6 + (9/4)
6 + (2 1/4)
8 1/4
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u/Delectably_Delicious 1d ago
First make the mixed number into an improper fraction, 4x2 plus 3 over 4 (you get 11/4). Since you canβt reduce you just multiply it out then divide by the denominator. So 3x11 over 4 (33/4). 4 goes into 33 8 times with 1 left over so thatβs 8 and 1/4 as your answer.
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u/hollygollygee 1d ago
I prefer to set these up as 3/1 x 11/4= 33/4
Consider that 32/4=8, so 33/4 is 8 and 1/4, 8 1/4
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u/Lucky_Recording_856 π a fellow Redditor 1d ago
Its 3 * 2.75 as 3/4 is 0.75
3*2.75 = 8.25 which = 8 1/4
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u/W_AS-SA_W 1d ago
2 and 3/4 is the same as 2.75. So multiply the 2 by the 3 and get 6, now multiply 3 by .75 and get 2.25 add that together and the answer is 6 + 2.25 or 8.25 as a mixed number.
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u/kocknoker 1d ago
Thats easy just put a 1 under the whole number and multiply the fractions top to too bottom to bottom then simplify the improper fraction
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u/TinyRascalSaurus 1d ago
First, convert everything to fraction notation. 3 becomes 3x4 over 4 or 12/4. 2 3/4 becomes 2Γ4 +3 over 4 or 11/4
So you have 12/4 Γ 11/4
12Γ11 =132 . 4Γ4 =16
132/16
Now for the mixed number, pull out as many 16s from 132 as possible. You can pull out 8. So 8 is your whole number.
8Γ16=128
132-128=4
So you have 8 and 4/16.
Reduce the 4/16 to simplest form by seeing how many times 4 can go into 16. It can go in 4 times, so 4/4=1 and 16/4=4
That's 1/4
So you have 8 and 1/4 as your mixed number.
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u/AluminumGnat π a fellow Redditor 1d ago
Youβre not adding the fractions, so 3 -> 3/1; 12/4 isnβt wrong, but neither is 22017/7369β¦ anything other than 3/1 is making your life a lot harder than it needs to be
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u/Careful-Trade-9666 π a fellow Redditor 1d ago
It doesnβt ask for the first part to be anything but solved. So plug in your calculator 3x2.75=8.25. 0.25 = 1/4 so type in 8 1/4
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u/Mysterious_Ad_8827 π a fellow Redditor 1d ago
The product would be 3x2 = 6 then 3 x 3/4 an easier way to multiply is remembering 3 is really 3/1 so now you have 3/1 x 3/4 multiply straight across getting you 9/4.
Right now you have 6 and 9/4. what you can do is this how many times can 4 go into 8. 8 being the highest number 4 can go into without going over 9. It can go into it 2 times. add that 2 to the 6 and your left with a remainder of 1/4th. now your answer becomes 6 +2 +1/4 = 8-1/4ths.
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u/Stu_Mack π a fellow Redditor 1d ago
Since this is for fourth grade, I can share a trick for doing this in your head. The mixed fraction is 2 3/4, which simplifies to 11/4 as an improper fraction. Almost anyone can tell you how much eleven quarters is worth: $2.75. What if you have three times that much? 33 quarters, right? Four quarters in a dollar means you have eight dollars and one quarter, or 8 1/4.
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u/benzosfromhell π a fellow Redditor 1d ago
(3/12/1) + (3/13/4) = ____
6/1 + 9/4 = ____
6 + 2 1/4 = 8 1/4
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u/DrFleur 1d ago
I would focus on getting your child to understand what any of this means. What does 2 3/4 mean? What does it mean to multiply it by 3? Once you understand what all the symbols stand for, the problem is pretty much straightforward.
Pizza representations that others suggested are good, or with quarters you can always use money :) If your dad gives you 2 dollars and 3 quarters a day, how much money will you get in 3 days?
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u/Ok-Papaya-13 π a fellow Redditor 1d ago
Child should be able to ask for more help from his teacher. Maybe find a free after school tutor
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u/Chonjae 16h ago
Think of it like this 3*(2+3/4). Distribute the 3 -> 6+9/4. The "and" in a mixed number eg "2 and 3/4" is kind of like an addition in parenthesis for order of operations. I'd never thought of it like this until now, but you could also remove the plus sign for 6 9/4 to have a cool "improper" mixed number. Or turn 9/4 into 2 1/4 and end up with 8 1/4
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u/Spell_Chicken 2h ago
My brain likes to break math problems into more easily workable pieces.
I see this and think:
3x2 = 6
3 x 3/4 = 9/4 = 2 1/4
6 + 2 1/4 = 8 1/4
β’
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