Envision Math 2.0: Grade 6, Volume 1
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6. Divide Mixed Numbers
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Exercise 32 Page 48

First, find the amount of teaspoons of vanilla that Margaret uses to make 1 cupcake. Then, multiply that amount by 30.

4 38 teaspoons

Practice makes perfect

We are told that Margaret uses 1 34 teaspoons of vanilla to make 12 vanilla cupcakes.

We are asked to find how much vanilla she will use to make 30 cupcakes. Let's first find the amount of vanilla that she uses to make 1 vanilla cupcake.

1 Vanilla Cupcake

Margaret uses 1 34 teaspoons of vanilla to make 12 cupcakes, so the amount of vanilla needed for only one cupcake is 1 34 divided by 12. 12cupcakes=1 34teaspoons ⇓ 1cupcake=1 34 teaspoons÷ 12The first step to calculating the quotient on the right-hand side is to write the mixed number as a fraction. Let's do it!
1 34Ă· 12
1* 4+ 3/4Ă· 12
4+ 3/4Ă· 12
7/4Ă· 12
7/4Ă· 12/1
Next, to divide by a fraction, we multiply by its reciprocal. 7/4Ă· 12/1=7/4* 1/12 Let's multiply the fractions!
7/4*1/12
7*1/4* 12
7/48
We found that Margaret needs 7 48 teaspoons of vanilla to make 1 cupcake. Now, let's find the amount of vanilla needed to make 30 cupcakes.

30 Cupcakes

We found that to make 1 cupcake, Margaret needs 7 48 teaspoons of vanilla. 1cupcake=7/48teaspoons This means that in order to make 30 cupcakes, she will need 30* 7 48 teaspoons of vanilla. 1cupcake=7/48teaspoons ⇓ 30cupcakes= 30* 7/48teaspoons Let's calculate this product!
30* 7/48
30/1* 7/48
30* 7/1* 48
210/48
We can write this fraction as a mixed number.
210/48
192+18/48
192/48+18/48
4+18/48
4+18Ă· 6/48Ă· 6
4+3/8
4 38
We calculated the product! 30cupcakes=30* 7/48teaspoons ⇕ 30cupcakes=4 38teaspoons We found that Margaret will use 4 38 teaspoons of vanilla to make 30 cupcakes.