Solve for the Undistributed Fraction

Question

A local supermarket distributes small pumpkins to its two chain store for fall season decorations. Store 1 gets 40 pumpkins. After distributing 4/7 of the leftover to Store 2, there are 24 pumpkins undistributed. What is the fraction of undistributed pumpkins of the total pumpkins?

Answer 1

Hi Daniel,

This is a fun question. It might be a little scary because it has fractions in it, but we can figure it out.

Let's start by making a list of the information that we know... and you might want to leave some space (a line or two) to come back and add information that we figure out.

Store 1: 40 pumpkins

Store 2: unknown number of pumpkins but we know that it is 4/7 of what remains. So for this, let's draw 4 boxes (or spaces) in a row that will each hold the same number (after we figure out what it is). __ __ __ __

Undistributed: 24 pumpkins __ __ __ (explanation below)

I'm not sure what your prior knowledge of fractions is, but I'm going to pretend like you don't know anything because others will read this post as well and may benefit from the explanation. The reason we put four spaces for the unknown number of pumpkins was because they represent 4/7 of what was left. So the undistributed number of pumpkins represents 3/7 of what was left (not of the total which is what we need to find).

You might wonder where I got the 3.... Well... let's pretend that you and your friend are eating cake and we cut it into 7 pieces. You were very kind and told your friend to take the number of pieces that he or she wanted. Your friend decided to take 4 pieces. How many would be left for you? (Three, right? And you got that by subtracting 4 from 7). That is the same reason we are going to go back to the undistributed number of pumpkins and draw 3 boxes or spaces that will hold the same number as the spaces for store 2. I'll do that now.

Now we have some information to help us figure out what number goes in the spaces. There are 24 undistributed pumpkins... what number when added together three times equals 24? Or what number times 3 equals 24? Hopefully you got 8. Put 8 in all of the spaces.

So store 1 had 40 pumpkins, store 2 had (8+8+8+8) pumpkins and there were 24 undistributed pumpkins.

Now the question is, what fraction of the total (store 1 + store 2 + undistributed) was undistributed? You'll need to add the total and then put 24 in the numerator and the total in the denominator. There will be some reducing to do.

Answer 2

Daniel

Answer: 1/4

This is really 2 separate problems. Let's forget about store 1 for a minute and just focus on the pumpkins in store 2 + the undistributed pumpkins.

The total pumpkins (store 2 + leftovers) we can write as 7/7 representing 100% of them

We know store 2 has 3/7 (24 pumpkins) so we have 4/7 leftover

Next it is helpful to set up a proportion: 3/7= 24/x

we get x=56, so now we know the total number of pumpkins in store 2 + the leftovers = 56

Time for the next part. Let's look back at store 1.

(56 + 40 = 96) so store 1 + store 2 + leftover = 96 pumpkins in all

24 undistributed pumpkins / 96 total pumpkins is the fraction you're looking for, you can reduce this fraction to 1/4 (both the numerator and denominator are divisible by 24)

If you would like further instructions in proportions, fractions, or multistep word problems I am happy to help!

-Ms. Maria

Answer 3

Hi Daniel,

After distributing 4/7 of the leftover to Store 2, 24 pumpkin are Undistributed.

Let's draw a bar chart based on this fraction given;

[_] represents 1 unit

Store 2 [_][_][_][_]

Undistributed [_][_][_]

Since Undistributed has 3 units for 24 pumpkins;

1 unit has 8 pumpkins (24÷3)_.

Therefore,

Store 2 and Undistributed totals, 8X7 = 56

Now, you know that Store 1 received 40 pumpkins.

Therefore,

Total Pumpkins = 56 + 40 = 96

Undistributed/ Total = 24/96

Simplify; 1/4

Final Answer is 1/4

To further illustrate the final answer;

Store 1 [8][8]][8][8][8] =>40

Store 2 [8][8]][8][8] =>32

Undistributed [8][8]][8] =>24

There are 12 units [8] here.

Undistributed is 3 units out of 12.

This confirms the answer is correct, 3/12 = 1/4