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Math  /  Numbers & Operations

Question8 or 10
Kate's new juicer is able to squeeze 34\frac{3}{4} of a cup of orange juice from 112\frac{1}{12} of a bag of oranges. Compute the unit rate of cups per bag of oranges.
A 3 cups per bag
B 6 cups per bag
C 9 cups per bag
D 12 cups per bag

Studdy Solution

STEP 1

What is this asking? Find out how many cups of orange juice Kate can get from one whole bag of oranges. Watch out! Don't mix up the fraction of the bag with the fraction of the cup!

STEP 2

1. Understand the given rate
2. Calculate the unit rate

STEP 3

Alright, let's break this down!
We know that Kate's juicer can squeeze 34\frac{3}{4} of a cup of orange juice from 112\frac{1}{12} of a bag of oranges.
This means that for every 112\frac{1}{12} of a bag, we get 34\frac{3}{4} of a cup.
It's like a mini conversion rate!

STEP 4

Now, we need to find out how many cups of juice we get from one full bag of oranges.
To do this, we need to figure out how many 112\frac{1}{12} parts are in a whole bag.
Since a whole bag is 11, we divide 11 by 112\frac{1}{12}:
1÷112=1⋅121=121 \div \frac{1}{12} = 1 \cdot \frac{12}{1} = 12So, there are **12** parts of 112\frac{1}{12} in one whole bag.

STEP 5

Next, we multiply the number of parts by the amount of juice each part gives us.
Each 112\frac{1}{12} of a bag gives us 34\frac{3}{4} of a cup.
So, we multiply:
12⋅34=12⋅34=364=912 \cdot \frac{3}{4} = \frac{12 \cdot 3}{4} = \frac{36}{4} = 9This means Kate can get **9** cups of juice from one full bag of oranges!

STEP 6

The unit rate is **9 cups per bag** of oranges.

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