Envision Math 2.0: Grade 6, Volume 1
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6. Divide Mixed Numbers
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Exercise 36 Page 48

Practice makes perfect
We are told that a restaurant has 15 15 pounds of ground beef for meat loaves and that each meat loaf requires 2 38 pounds of ground beef. We want to find the number of meat loaves that can be made. Meat loaves= ? We can find this information if we divide 15 15 by 2 38. Meat loaves= 15 15Ă· 2 38 First, let's write each mixed number as a fraction.
15 15Ă· 2 38
15* 5+1/5Ă· 2*8+3/8
75+1/5Ă· 16+3/8
76/5Ă· 19/8
Next, to divide by a fraction, we multiply by its reciprocal. 76/5Ă· 19/8=76/5* 8/19 Let's multiply the fractions!
76/5* 8/19
76* 8/5* 19
608/95
Now we will write this as a mixed number.
608/95
570+38/95
570/95+38/95
6+38/95
6+38Ă· 19/95Ă· 19
6+2/5
6 25
We found that the restaurant can make 6 25 meat loaves. The restaurant will not make a fraction of a meat loaf, so we can conclude that the restaurant can actually make 6 meat loaves.
In Part A, we found that the restaurant can make 6 larger size meat loaves. We are asked to find how many more smaller meat loaves — which each use 1 35 pounds of ground beef — the restaurant can make. This means that we need to find the following difference. 6-Number of smaller meat loaves= ? Let's find the number of smaller meat loaves that the restaurant can make! Like we did before, let's divide the total ground beef, 15 15 pounds, by the size of a smaller meat loaf, 1 35 pounds. Number of smaller meat loaves=15 15÷ 1 35 Let's calculate this quotient! First, we will write the mixed numbers as fractions.
15 15Ă· 1 35
15*5 +1/5Ă· 1* 5+3/5
75 +1/5Ă· 5+3/5
76/5Ă· 8/5
Next, we will multiply by the reciprocal of the divisor. 76/5Ă· 8/5=76/5* 5/8 Let's multiply the fractions!
76/5* 5/8
76* 5/5* 8
380/40
Now we can write this fraction as a mixed number.
380/40
360+20/40
360/40+20/40
9+1/2
9 12
We found that the restaurant can make 9 12 smaller meat loaves. The restaurant would not make a fraction of a meat loaf, so we can conclude that they can make 9 smaller meat loaves. Finally, let's calculate the difference between the numbers of smaller and larger meat loaves. Smaller loaves- Larger loaves ⇓ 9- 6=3 We found that the restaurant can make 3 more smaller meat loaves than the larger meat loaves.