All the solutions provided in **McGraw Hill Math Grade 5 Answer Key PDF Chapter 9 Lesson 12 Subtract Mixed Numbers** will give you a clear idea of the concepts.

## McGraw-Hill My Math Grade 5 Answer Key Chapter 9 Lesson 12 Subtract Mixed Numbers

**Math in My World**

Example 1

One King crab weighs 2\(\frac{3}{4}\) pounds. A second King crab weighs 1\(\frac{1}{4}\)– pounds. How much more does the one King crab weigh? Use models to find the difference.

Find 2\(\frac{3}{4}\) – 1\(\frac{1}{4}\)

Estimate 3 – 1 = ____

Model 2\(\frac{3}{4}\) using fraction tiles.

Subtract 1\(\frac{1}{4}\) by crossing out 1 whole and one \(\frac{1}{4}\)-tile.

There is one whole and two \(\frac{1}{4}\)-tiles left,

which is 1\(\frac{2}{4}\), or

So, 2\(\frac{3}{4}\) – 1\(\frac{1}{4}\) = .

The first King crab weighs pounds more than the second.

Check for Reasonableness ____ ≈

Answer:

we need to find 2 3/4 – 1 1/4

estimate: 3 – 1 = 2

simplify the equation:

= 2 – 1 – 3/4 – 1/4

= 1 – 2/4

= 1 – 1/2

= 1 1/2.

so, 2\(\frac{3}{4}\) – 1\(\frac{1}{4}\) =

The first crab weighs, pounds more than the second.

check for reasonable: 2 ≈

Example 2

Find 6\(\frac{11}{16}\) – 2\(\frac{5}{8}\)

Estimate 7 – 3 = 4

1. Write an equivalent fraction for 2\(\frac{5}{8}\) so that the fractions have the same denominator. The LCD is 16.

2. Subtract the wholes. Then subtract the fractions.

So, 6\(\frac{11}{16}\) – 2\(\frac{5}{8}\) =

Check for Reasonableness ___4_____ ≈

**Talk Math**

Describe the steps you would take to find 3\(\frac{5}{8}\) – 2\(\frac{3}{8}\).

The above-given equation:

3 5/8 – 2 3/8

In the first step, we separate the whole numbers and the fractions.

The equation is: 3 – 2 – 5/8 – 3/8

In the second step:

simplify the equation and check whether the denominators are the same.

denominators are equal so we can subtract directly.

= 1 – 2/8

= 1 – 1/4

= 1 1/4.

Therefore, 3 5/8 – 2 3/8 = 1 1/4.

**Guided Practice**

**Estimate, then subtract. Write each difference in simplest form.**

Question 1.

Answer:

The above-given mixed fractions:

4 2/3 – 2 1/3

Here the denominators are equal so we can subtract directly.

= 4 – 2 – 2/3 – 1/3

= 2 – 1/3

This can be written as 2 1/3.

Therefore,

Question 2.

Answer:

The above-given mixed fractions:

5 4/5 – 3 2/5

= 5 – 3 – 4/5 – 2/5

= 2 – 4/5 – 2/5

Here the denominators are equal so we can subtract directly.

= 2 – 2/5

This can also be written as 2 2/5.

Therefore,

**Independent Practice**

**Estimate, then subtract. Write each difference in simplest form.**

Question 3.

Answer:

The above-given mixed fractions:

5 3/4 – 2 1/2

= 5 – 2 – 3/4 – 1/2

= 3 – 3/4 – 1/2

Here denominators are not equal so we have to make the denominators equal.

– Find the common denominator.

– 4 is the least common multiple of denominators 4 and 2. Use it to convert to equivalent fractions with this common denominator.

= 3 – (3 – 2)/4

= 3 – 1/4

This can also be written as 3 1/4

Therefore,

Question 4.

Answer:

The above-given mixed fractions:

6 5/7 – 3 3/7

Here the denominators are equal so we can subtract directly.

= 6 – 3 – 5/7 – 3/7

= 3 – 2/7

This can also be written as 3 2/7.

Therefore,

Question 5.

Answer:

The above-given mixed fractions:

7 8/9 – 5 1/3

= 7 – 5 – 8/9 – 1/3

here the denominators are not equal so we have to make the denominators equal.

– Find the common denominator.

– 9 is the least common multiple of denominators 9 and 3. Use it to convert to equivalent fractions with this common denominator.

= 2 – (8 – 3)/9

= 2 – 5/9

This can also be written as 2 5/9.

Question 6.

Answer:

The above-given mixed fractions:

15 11/12 – 4 1/3

= 15 – 4 – 11/12 – 1/3

here the denominators are not equal so we have to make the denominators equal.

– Find the common denominator.

– 12 is the least common multiple of denominators 12 and 3. Use it to convert to equivalent fractions with this common denominator.

= 11 – (11 – 4)/12

= 11 – 7/12

This can also be written as 11 7/12.

Question 7.

Answer:

The above-given mixed fractions:

13 9/10 – 4 2/5

= 13 – 4 – 9/10 – 2/5

here the denominators are not equal so we have to make the denominators equal.

– Find the common denominator.

– 10 is the least common multiple of denominators 10 and 5. Use it to convert to equivalent fractions with this common denominator.

= 9 – (9 – 4)/10

= 9 – 5/10

= 9 – 1/2

This can also be written as 9 1/2.

Question 8.

Answer:

The above-given mixed fractions:

12 5/6 – 7 1/3

= 12 – 7 – 5/6 – 1/3

= 5 – 5/6 – 1/3

here the denominators are not equal so we have to make the denominators equal.

– Find the common denominator.

– 6 is the least common multiple of denominators 6 and 3. Use it to convert to equivalent fractions with this common denominator.

= 5 – (5 – 2)/6

= 5 – 3/6

= 5 – 1/2

= 5 1/2

Therefore,

Question 9.

8\(\frac{3}{8}\) – 2\(\frac{1}{4}\) = _____

Answer:

The above-given mixed fractions:

8 3/8 – 2 1/4

= 8 – 2 – 3/8 – 1/4

= 6 – 3/8 – 1/4

here the denominators are not equal so we have to make the denominators equal.

– Find the common denominator.

– 8 is the least common multiple of denominators 8 and 4. Use it to convert to equivalent fractions with this common denominator.

= 6 – (3 – 2)/8

= 6 – 1/8

This can also be written as 6 1/8

Therefore, 8\(\frac{3}{8}\) – 2\(\frac{1}{4}\) = 6 1/8

Question 10.

7\(\frac{7}{8}\) – 4\(\frac{1}{2}\) = _____

Answer:

The above-given mixed fractions:

7 7/8 – 4 1/2

= 7 – 4 – 7/8 – 1/2

= 3 – 7/8 – 1/2

here the denominators are not equal so we have to make the denominators equal.

– Find the common denominator.

– 8 is the least common multiple of denominators 8 and 2. Use it to convert to equivalent fractions with this common denominator.

= 3 – (7 – 4)/8

= 3 – 2/8

= 3 – 1/4

This can also be written as 3 1/4

Therefore, 7\(\frac{7}{8}\) – 4\(\frac{1}{2}\) = 3 1/4

Question 11.

12\(\frac{7}{10}\) – 7\(\frac{2}{5}\) = _____

Answer:

The above-given mixed fractions:

12 7/10 – 7 2/5

= 12 – 7 – 7/10 – 2/5

= 5 – 7/10 – 2/5

here the denominators are not equal so we have to make the denominators equal.

– Find the common denominator.

– 10 is the least common multiple of denominators 10 and 2. Use it to convert to equivalent fractions with this common denominator.

= 5 – (7 – 4)/10

= 5 – 3/10

This can also be written as 5 3/10.

Therefore, 12\(\frac{7}{10}\) – 7\(\frac{2}{5}\) = 5 3/10.

**Mathematical Practice 2 Use Algebra Find each unknown.**

Question 12.

11\(\frac{11}{12}\) – 2\(\frac{1}{12}\) = x

x = _____

Answer:

The above-given mixed fractions:

11 11/12 – 2 1/12 = x

we need to find out the x value.

11 – 2 – 11/12 – 1/12

Here denominators are the same. So we can subtract directly.

x = 9 – (11 – 1)/12

x = 9 – 10/12 { in 2nd table 2 x 5 = 10; 2 x 6 = 12}

x = 9 – 5/6

This can also be written as 9 5/6

Therefore, the value of x is 9 5/6.

Question 13.

14\(\frac{9}{14}\) – 5\(\frac{2}{7}\) = c

c = _____

Answer:

The above-given mixed fractions:

14 9/14 – 5 2/7 = c

we need to find the c value.

c = 14 – 5 – 9/14 – 2/7

c = 9 – 9/14 – 2/7

here the denominators are not equal so we have to make the denominators equal.

– Find the common denominator.

– 14 is the least common multiple of denominators 14 and 7. Use it to convert to equivalent fractions with this common denominator.

c = 9 – (14 – 4)/14

c = 9 – 10/14

c = 9 – 5/7

This can also be written as 9 5/7.

Therefore, the value of c is 9 5/7.

Question 14.

18\(\frac{11}{15}\) – 9\(\frac{2}{5}\) = n

n = _____

Answer:

The above-given mixed fractions:

18 11/15 – 9 2/5 = n

we need to find the n value.

n = 18 – 9 – 11/15 – 2/5

Here the denominators are the same so we can subtract directly.

n = 9 – (11 – 2)/5

n = 9 – 9/5

This can also be written as 9 9/5.

Therefore, the value of n is 9 9/5.

**Problem Solving**

Question 15.

The length of Mr Cho’s garden is 8\(\frac{5}{6}\) feet. Find the width of Mr Cho’s garden if it is 3\(\frac{1}{6}\) feet less than the length.

Answer:

The above-given:

The length of the Cho’s garden in feet = 8 5/6

we need to find the width. Let it be w.

The other fraction is 3 1/6

Based on the given conditions, formulate:

8 5/6 – 3 1/6

= 8 – 3 – 5/6 – 1/6

= 5 – 5/6 – 1/6

Here denominators are the same so we can subtract directly.

w = 5 – (5 – 1)/6

w = 5 – 4/6

w = 5 – 2/3

This can also be written as 5 2/3.

Therefore, the width is 5 2/3 feet.

Question 16.

Timberly spent 3\(\frac{4}{5}\) hours and Misty spent 2\(\frac{1}{10}\) hours at gymnastics practice over the weekend. How many more hours did Timberly spend than Misty at gymnastics practice?

Answer:

The above-given:

The number of hours Timberly spent at gymnastics = 3 4/5

The number of hours Misty spent at gymnastics = 2 1/10

The number of more hours Timberly spent than Misty = g

g = 3 4/5 – 2 1/10

g = 3 – 2 – 4/5 – 1/10

g = 1 – 4/5 – 1/10

here the denominators are not equal so we have to make the denominators equal.

– Find the common denominator.

– 10 is the least common multiple of denominators 5 and 10. Use it to convert to equivalent fractions with this common denominator.

g = 1 – (8 – 1)/10

g = 1 – 7/10

This can also be written as 1 7/10

Therefore, Timberly spent 1 7/10 hours more than Misty.

Question 17.

**Mathematical PRACTICE 1 Make Sense of Problems** Warner lives 9\(\frac{1}{4}\)– blocks away from the ocean. Shelly lives 12\(\frac{7}{8}\) blocks away from the ocean. How many more blocks does Shelly live away from the ocean than Warner?

Answer:

The above-given:

The number of blocks away from Warner lives = 9 1/4

The number of blocks away from the ocean Shelly lives = 12 7/8

The number of blocks Shelly lives away from the ocean than Warner = o

o = 12 7/8 – 9 1/4

o = 12 – 9 – 7/8 – 1/4

o = 3 – 7/8 – 1/4

here the denominators are not equal so we have to make the denominators equal.

– Find the common denominator.

– 8 is the least common multiple of denominators 8 and 4. Use it to convert to equivalent fractions with this common denominator.

o = 3 – (7 – 2)/8

o = 3 – 5/8

This can also be written as 3 5/8

Therefore, she lives 3 5/8 blocks away from the ocean than a warner.

**HOT Problems**

Question 18.

**Mathematical PRACTICE 4 Model Math** Write a real-world problem involving the subtraction of two mixed numbers whose difference is less than 2\(\frac{1}{2}\). Then solve.

Answer:

The two mixed numbers are x and y

x – y < 2 1/2

a sample answer is given:

One King crab weighs 2\(\frac{3}{4}\) pounds. A second King crab weighs 1\(\frac{1}{4}\)– pounds. How much more does the one King crab weigh?

Now subtract 2 3/4 and 1 1/4

2 3/4 – 1 1/4

= 2 – 1 – 3/4 – 1/4

= 1 – 2/4

= 1 – 1/2

This can also be written as 1 1/2

1 1/2 < 2 1/2

Therefore, 2 3/4 – 1 1/4 < 2 1/2.

Question 19.

**? Building on the Essential Question** How can number sense help to know if I have subtracted two mixed numbers correctly?

Answer:

You could first convert each to an improper fraction. If they don’t have common denominators, then find a common denominator and use it to rewrite each fraction. Then subtract the fractions and compare the given mixed fractions. So that we can easily find out.

### McGraw Hill My Math Grade 5 Chapter 9 Lesson 12 My Homework Answer Key

**Practice**

**Estimate, then subtract. Write each difference in simplest form.**

Question 1.

Answer:

The above-given mixed fractions:

6 5/8 – 2 3/8

= 6 – 2 – 5/8 – 3/8

Here denominators are the same so that we can subtract directly.

= 4 – (5 – 3)/8

= 4 – 2/8

= 4 – 1/4

This can also be written as 4 1/4

Therefore, 6 5/8 – 2 3/8 = 4 1/4

Question 2.

Answer:

The above- is given:

9 3/4 – 1 1/3

= 9 – 1 – 3/4 – 1/3

here the denominators are not equal so we have to make the denominators equal.

– Find the common denominator.

– 12 is the least common multiple of denominators 4 and 3. Use it to convert to equivalent fractions with this common denominator.

= 8 – (9 – 4)/12

= 8 – 5/12

This can also be written as 8 5/12.

Question 3.

Answer:

The above-given mixed fractions:

4 5/6 – 4 1/3

= 4 – 4 – 5/6 – 1/3

here the denominators are not equal so we have to make the denominators equal.

– Find the common denominator.

– 6 is the least common multiple of denominators 6 and 3. Use it to convert to equivalent fractions with this common denominator.

= 0 – (5 – 2)/6

= 3/6

= 1/2

Therefore, the answer is 1/2

**Problem Solving**

Question 4.

Mrs Gabel bought 7\(\frac{5}{6}\) gallons of punch for the class party. The students drank 4\(\frac{1}{2}\) gallons of punch. How much punch was left at the end of the party? Write in simplest form.

Answer:

The above-given:

The number of gallons of punch Gabel bought for the party = 7 5/6

The number of gallons of punch students drank = 4 1/2

The number of gallons of punch left = p

p = 7 5/6 – 4 1/2

p = 7 – 4 – 5/6 – 1/2

p = 3 – 5/6 – 1/2

here the denominators are not equal so we have to make the denominators equal.

– Find the common denominator.

– 6 is the least common multiple of denominators 6 and 2. Use it to convert to equivalent fractions with this common denominator.

p = 3 – (5 – 3)/6

p = 3 – 2/6

p = 3 – 1/3

This can also be written as 3 1/3

Therefore, 3 1/3 gallons of punch was left at the end of the party.

Question 5.

Bella is 10\(\frac{5}{12}\) years old. Franco is 12\(\frac{7}{12}\) years old. What is the difference in their ages? Write in simplest form.

Answer:

The above-given:

The number of years old the Bella is = 10 5/12

The number of years old Franco was = 12 7/12

The difference in their ages = a

a = 12 7/12 – 10 5/12

Here denominators are the same so we have to subtract directly.

a = 12 – 10 – 7/12 – 5/12

a = 2 – (7 – 5)/12

a = 2 – 2/12

a = 2 – 1/6

a = 2 1/6.

Therefore, the difference is 2 1/6

Question 6.

In one week, the fifth grade class recycled 9\(\frac{2}{3}\) pounds of glass and 12\(\frac{3}{4}\) pounds of newspaper. How many more pounds of a newspaper than glass did the class recycle?

Answer:

The above-given:

The number of pounds of glass recycled by the fifth grade = 9 2/3

The number of pounds of newspapers recycled = 12 3/4

The number of more pounds of newspaper recycled than glass = R

R = 12 3/4 – 9 2/3

R = 12 – 9 – 3/4 – 2/3

R = 3 – 3/4 – 2/3

here the denominators are not equal so we have to make the denominators equal.

– Find the common denominator.

– 12 is the least common multiple of denominators 3 and 4. Use it to convert to equivalent fractions with this common denominator.

R = 3 – (9 – 8)/12

R = 3 – 1/12

R = 3 1/12

Therefore, 3 1/4 pounds of the newspaper is recycled than glass.

Question 7.

**Mathematical PRACTICE 2 Use Number Sense** A snack mix recipe calls for 5\(\frac{3}{4}\) cups of cereal and 3\(\frac{5}{12}\) cups less of raisins. How many cups of raisins are needed? Write in simplest form.

Answer:

The above-given:

The number of cups of cereal mixed for a snack = 5 3/4

The number of cups of raisins less = 3 5/12

The number of cups of raisins needed = c

c = 5 3/4 – 3 5/12

c = 5 – 3 – 3/4 – 5/12

c = 2 – 3/4 – 5/12

here the denominators are not equal so we have to make the denominators equal.

– Find the common denominator.

– 12 is the least common multiple of denominators 4 and 12. Use it to convert to equivalent fractions with this common denominator.

c = 2 – (9 – 5)/12

c = 2 – 4/12

c = 2 – 1/3

c = 2 1/3

Therefore, 2 1/3 cups of raisins are needed.

**Test Practice**

Question 8.

What is the difference between the two weights?

A. \(\frac{1}{2}\) ounce

B. \(\frac{7}{8}\) ounce

C. 1\(\frac{3}{8}\) ounces

D. 1\(\frac{7}{8}\) ounces

Answer: Option C is the correct answer

Explanation:

The above-given weights:

The weight of the phone = 4 1/2

The weight of the remote = 3 1/8

The difference between the objects = d

d = 4 1/2 – 3 1/8

d = 4 – 3 – 1/2 – 1/8

d = 1 – 1/2 – 1/8

here the denominators are not equal so we have to make the denominators equal.

– Find the common denominator.

– 8 is the least common multiple of denominators 2 and 8. Use it to convert to equivalent fractions with this common denominator.

d = 1 – (4 – 1)/8

d = 1 – 3/8

d = 1 3/8

Therefore, the difference between the weights is 1 3/8 ounces.