All the solutions provided in **McGraw Hill Math Grade 5 Answer Key PDF Chapter 9 Lesson 11 Add Mixed Numbers** will give you a clear idea of the concepts.

## McGraw-Hill My Math Grade 5 Answer Key Chapter 9 Lesson 11 Add Mixed Numbers

**Math in My World**

Example 1

A hammerhead shark swam 2\(\frac{1}{4}\) miles. The next day, it swam 1\(\frac{1}{4}\) miles. How many miles did it swim altogether?

Find 2\(\frac{1}{4}\) + 1\(\frac{1}{4}\).

Estimate 2\(\frac{1}{4}\) + 1\(\frac{1}{4}\) ≈ 2 + 1, or 3

2\(\frac{1}{4}\) + 1\(\frac{1}{4}\) = 1 + 1 + \(\frac{1}{4}\) + 1 + \(\frac{1}{4}\) Write as a sum of wholes and fractions.

= 1 + 1 + 1 + \(\frac{1}{4}\) + \(\frac{1}{4}\) Group the wholes and the fractions together.

= 3 + \(\frac{2}{4}\) 1 + 1 + 1 = 3 and \(\frac{1}{4}\) + \(\frac{1}{4}\) = \(\frac{2}{4}\)

= Write in simplest form. \(\frac{2}{4}\) = \(\frac{1}{2}\)

So, the hammerhead shark swam miles.

The models show that 2\(\frac{1}{4}\) + 1\(\frac{1}{4}\) = 3\(\frac{1}{2}\)

Check Compared to the estimate, 3\(\frac{1}{2}\) ≈ 3. The answer is reasonable.

Answer:

The process is given above:

The number of miles hammerhead shark swim = 2 1/4

The number of miles hammerhead sharks swim on the next day = 1 1/4

The total number of miles a shark travels altogether = X

X = 2 1/4 + 1 1/4

X = 2 + 1 + 1/4 + 1/4

X = 3 + 2/4

X = 3 + 1/2

X = 3 1/2.

Therefore, the shark travels altogether is miles.

Example 2

The diagram shows the length of a sea turtle. What is the total length of the sea turtle?

Find \(\frac{7}{8}\) + 3\(\frac{1}{4}\) + 1\(\frac{1}{8}\).

1. Write an equivalent fraction for 3\(\frac{1}{4}\) so that the fractions all have the same denominator. The LCD is 8.

Write an equivalent fraction with a denominator of 8.

2. Add.

\(\frac{7}{8}\) + 3\(\frac{1}{4}\) + 1\(\frac{1}{8}\) = \(\frac{7}{8}\) + 3\(\frac{2}{8}\) + 1\(\frac{1}{8}\) Write 3\(\frac{1}{4}\) as 3\(\frac{2}{8}\)

= 3 + 1 + \(\frac{7}{8}\) + \(\frac{2}{8}\) + \(\frac{1}{8}\) Group the wholes and the fractions together.

= 4 + \(\frac{10}{8}\) 3 + 1 = 4 and \(\frac{7}{8}\) + \(\frac{2}{8}\) + \(\frac{1}{8}\) = \(\frac{10}{8}\)

= 4 + 1\(\frac{2}{8}\) Write \(\frac{10}{8}\) as \(\frac{8}{8}\) + \(\frac{2}{8}\), or 1\(\frac{2}{8}\)

= Write in simplest form. 4 + 1 = 5 and \(\frac{2}{8}\) = \(\frac{1}{4}\)

So, \(\frac{7}{8}\) + 3\(\frac{1}{4}\) + 1\(\frac{1}{8}\) =

The total length of the sea turtle is feet.

**Guided Practice**

Question 1.

Estimate, then add. Write the sum in simplest form.

3\(\frac{3}{8}\) + 2\(\frac{1}{2}\) = 1 + 1 + 1 + \(\frac{3}{8}\) + 1 + 1 + \(\frac{4}{8}\).

=

Answer:

The above-given mixed fractions:

3 3/8 + 2 1/2

Now simplify the equation:

= 3 + 2 + 3/8 + 1/2

= 5 + 3/8 + 1/2

In fractions, make the denominators the same. So what we do is, take LCM.

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

= 5 + (3 + 4)/8

= 5 + 7/8

= 5 7/8

Therefore, 3\(\frac{3}{8}\) + 2\(\frac{1}{2}\) =

**Talk Math**

Explain how to simplify 3\(\frac{6}{4}\)

Answer:

Go through the step-by-step procedure given below to understand how to simplify fractions.

**Step 1: **Write the factors of the numbers which are there in the numerator and denominator.

**Step 2:** Identify the common factors of both the numerator and denominator.

**Step 3:** In this step, we have to divide the numerator and denominator by the common factors until they have no common factor other than 1.

The above-given fraction:

3 6/4

6/4 is not simplified 2 is a common factor of 6 and 4.

Note: After simplifying a fraction, it is always important to check the result to make sure that the numerator and denominator do not have any more factors in common. Remember, the definition of a simplified fraction: a fraction is considered simplified if there are no common factors in the numerator and denominator.

**Independent Practice**

**Estimate, then add. Write each sum in simplest form.**

Question 2.

4\(\frac{3}{5}\) + 3\(\frac{1}{5}\) = ____

Answer:

The above-given mixed fractions:

4 3/5 + 3 1/5

Here denominators are the same. So we can directly add the fractions.

= 4 + 3 + 3/5 + 1/5

= 7 + 4/5

= 7 4/5

Therefore, 4\(\frac{3}{5}\) + 3\(\frac{1}{5}\) =

Question 3.

7\(\frac{4}{11}\) + 2\(\frac{6}{11}\) = ____

Answer:

The above-given mixed fractions:

7 4/11 + 2 6/11

Here the denominators are the same. So we can add the fractions directly.

= 7 + 2 + 4/11 + 6/11

= 9 + 10/11

= 9 10/11

Therefore, 7\(\frac{4}{11}\) + 2\(\frac{6}{11}\) =

Question 4.

5\(\frac{1}{12}\) + 6\(\frac{1}{4}\) = ____

Answer:

The above-given mixed fractions:

5 1/2 + 6 1/4

Here the denominators are not the same. So we have to find the equivalent denominators.

– Find the common denominators:

= 5 + 6 + 1/2 + 1/4

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

= 11 + (2 + 1)/4

= 11 + 3/4

This can be written as 11 3/4

Therefore, 5\(\frac{1}{12}\) + 6\(\frac{1}{4}\) =

Question 5.

8\(\frac{4}{15}\) + 3\(\frac{2}{15}\) = ____

Answer:

The above-given mixed fractions:

8 4/15 + 3 2/15

Here denominators are the same. So we can directly add the fractions.

= 8 + 3 + 4/15 + 2/15

= 11 + 6/15

6/15 is not simplified because 3 is a common factor of 6 and 15.

Note: After simplifying a fraction, it is always important to check the result to make sure that the numerator and denominator do not have any more factors in common. Remember, the definition of a simplified fraction: a fraction is considered simplified if there are no common factors in the numerator and denominator.

Question 6.

6\(\frac{1}{9}\) + 2\(\frac{1}{3}\) = ____

Answer:

The above-given mixed fractions:

6 1/9 + 2 1/3

Here the denominators are not the same. So we have to find the equivalent denominators.

– Find the common denominators:

= 6 + 2 + 1/9 + 1/3

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

= 8 + (1 + 3)/9

= 8 + 4/9

= 8 4/9

Therefore, 6\(\frac{1}{9}\) + 2\(\frac{1}{3}\) =

Question 7.

5\(\frac{1}{3}\) + 6\(\frac{1}{2}\) = ____

Answer:

The above-given mixed fractions:

5 1/3 + 6 1/2

Here the denominators are not the same. So we have to find the equivalent denominators.

– Find the common denominators:

= 5 + 6 + 1/3 + 1/2

6 is the least common multiple of denominators 3 and 2. Use it to convert to equivalent fractions with this common denominator.

= 11 + (2 + 3)/6

= 11 + 5/6

= 11 5/6

Therefore, 5\(\frac{1}{3}\) + 6\(\frac{1}{2}\) =

Question 8.

Answer:

The above-given fractions:

3 4/9 + 4 2/3

Here the denominators are not the same. So we have to find the equivalent denominators.

– Find the common denominators:

= 3 + 4 + 4/9 + 2/3

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

= 7 + (4 + 6)/9

= 7 + 10/9

10/9 is an improper fraction so we need to convert it into a mixed fraction.

– 10 ÷ 9 = 1 remainder 1

= 7 + 1 1/9

= 8 1/9.

Therefore,

Question 9.

Answer:

The above-given mixed fractions:

6 3/4 + 3 1/8

Here the denominators are not the same. So we have to find the equivalent denominators.

– Find the common denominators:

= 6 + 3 + 3/4 + 1/8

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

= 9 + (6 + 1)/8

= 9 + 7/8

= 9 7/8

Therefore,

Question 10.

Answer:

The above-given mixed fractions:

4 3/7 + 7 1/2

Here the denominators are not the same. So we have to find the equivalent denominators.

– Find the common denominators:

= 4 + 7 + 3/7 + 1/2

14 is the least common multiple of denominators 7 and 2. Use it to convert to equivalent fractions with this common denominator.

= 11 + ( 6 + 7)/14

= 11 + 13/14

= 11 13/14.

Therefore,

**Algebra Find each unknown.**

Question 11.

9\(\frac{9}{10}\) + 7\(\frac{3}{5}\) = y

y = _____

Answer:

The above-given mixed fractions:

9 9/10 + 7 3/5 = y

Here the denominators are not the same. So we have to find the equivalent denominators.

– Find the common denominators:

y = 9 + 7 + 9/10 + 3/5

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

y = 16 + (9 + 6)/10

y = 16 + 15/10

15/10 = 3/2 {15/10 is not simplified because 5 is a common factor for 15 and 10}

3/2 in mixed fraction: 1 1/2

y = 16 + 1 1/2

y = 17 1/2.

Therefore, the value of y =

Question 12.

14\(\frac{19}{20}\) + 8\(\frac{1}{4}\) = k

k = _____

Answer:

The above-given fractions:

14 19/20 + 8 1/4 = k

Here the denominators are not the same. So we have to find the equivalent denominators.

– Find the common denominators:

k = 14 + 8 + 19/20 + 1/4

20 is the least common multiple of denominators 20 and 4. Use it to convert to equivalent fractions with this common denominator.

k = 22 + ( 19 + 5)/20

k = 22 + 24/20

24/20 is not simplified because 4 is a common factor for 24 and 20

24/20: if we divide by 4 then we get 6/5

6/5 is an improper fraction. So we have to convert it into a mixed fraction.

6 ÷ 5 = 1 remainder 1.

The mixed fraction is 1 1/5

k = 22 + 1 1/5

k = 23 1/5

Question 13.

16\(\frac{11}{12}\) + 5\(\frac{2}{3}\) = d

d = _____

Answer:

The above-given mixed fraction:

16 11/12 + 5 2/3 = d

Here the denominators are not the same. So we have to find the equivalent denominators.

– Find the common denominators:

d = 16 + 5 + 11/12 + 2/3

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

d = 21 + (11 + 8)/12

d = 21 + 19/12

19/12 is an improper fraction so we have to convert it into a mixed fraction.

19 ÷ 12 = 1 remainder 7

This can be written as 1 7/12

d = 21 + 1 7/12

d = 22 7/12.

**Problem Solving**

Question 14.

Zita made 1\(\frac{5}{8}\) quarts of punch. Then she made 1\(\frac{7}{8}\) more quarts. How much punch did she make in all?

Answer:

The above-given:

The number of quarts of punch Zita made = 1 5/8

The number of quarts of more punch she made = 1 7/8

The total punch she makes = p

p = 1 5/8 + 1 7/8

p = 1 + 1 + 5/8 + 7/8

p = 2 + 12/8

p = 2 + 3/2

p = 2 3/2

Therefore, the total punch is 2 3/2 quarts.

Question 15.

Find five and two-eighths plus three and six-eighths. Write in words in simplest form.

Answer:

This can be written as:

5 2/8 + 3 6/8

Now simplify the equation:

5 + 3 + 2/8 + 6/8

As the denominators are the same, so we can add directly.

= 8 + 8/8

= 8 + 1

= 9

In word form, nine.

Question 16.

**Mathematical PRACTICE 1 Make a Plan** Tomas made fruit salad using the recipe. How many cups of fruit are needed altogether?

Answer:

The above-given:

The number of cups of banana = 3 1/2

The number of cups of grapes = 1 1/4

The number of cups of strawberry = 1 3/4

The number of cups of pears = 2 1/4

The total number of cups of fruits he used = x

x = 3 1/2 + 1 1/4 + 1 3/4 + 2 1/4

x = 3 + 1 + 1 + 2 + 1/2 + 1/4 + 1/4 + 1/4

x = 7 + 1/2 + 3/4

Make the denominators equal.

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

x = 7 + (2 + 3)/4

x = 7 + 5/4

5/4 is an improper fraction so convert it into mixed fractions.

5/4 = 1 1/4

x = 7 + 1 1/4

x = 8 1/4

Therefore, he used 8 1/4 cups of fruit to make a fruit salad.

**HOT Problems**

Question 17.

**Mathematical PRACTICE 3 Find the Error** Antwan is finding 4\(\frac{1}{5}\) + 2\(\frac{3}{5}\). Find and correct his mistake.

Answer:

The above-given equation:

4 1/5 + 2 3/5

Now simplify the equation:

= 4 + 2 + 1/5 + 3/5

as the denominators are equal so we can directly add the fractions.

= 6 + 4/5

= 6 4/5

Therefore, 6 4/5 is the correct answer.

Question 18.

**? Building on the Essential Question** How can equivalent fractions help when adding mixed numbers?

Answer:

– It can help by when finding the LCD (Least Common Denominator) you find the least number they have in common then that number is your equivalent fraction.

* The least common denominator (LCD) is the smallest number that can be a common denominator for a set of fractions.

### McGraw Hill My Math Grade 5 Chapter 9 Lesson 11 My Homework Answer Key

**Practice**

**Estimate, then add. Write each sum in simplest form.**

Question 1.

2\(\frac{1}{10}\) + 5\(\frac{7}{10}\) = ____

Answer:

The above-given mixed fractions:

2 1/10 + 5 7/10

Now simplify the equation:

= 2 + 5 + 1/10 + 7/10

= 7 + 1/10 + 7/10

as the denominators are the same so we can directly add the fractions.

= 7 + 8/10

8/10 is not simplified because 2 is a common factor of 8 and 10.

8/10 = if we divide by 2 then we get 4/5

= 7 + 4/5

* A mixed fraction a b/c can also be written as a + (b/c).

= 7 4/5.

Therefore, 2\(\frac{1}{10}\) + 5\(\frac{7}{10}\) = 7 4/5.

Question 2.

9\(\frac{3}{4}\) + 8\(\frac{3}{4}\) = ____

Answer:

The above-given mixed fractions:

9 3/4 + 8 3/4

= 9 + 8 + 3/4 + 3/4

= 17 + 6/4

6/4 is divided by 2 because 2 is a common factor of 6 and 4.

6/4 = 3/2

= 17 + 3/2

3/2 is an improper fraction so convert it into a mixed fraction.

3/2 = 1 remainder = 1

3/2 in the mixed fraction is 1 1/2

Finally, 17 + 1 1/2

= 18 1/2

Therefore, 9\(\frac{3}{4}\) + 8\(\frac{3}{4}\) = 18 1/2.

Question 3.

3\(\frac{5}{8}\) + 6\(\frac{1}{2}\) = ____

Answer:

The above-given mixed fraction:

3 5/8 + 6 1/2

= 3 + 6 + 5/8 + 1/2

Here the denominators are not the same. So we have to find the equivalent denominators.

– Find the common denominators:

= 9 + 5/8 + 1/2

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

= 9 + ( 5 + 4)/8

= 9 + 9/8

9/8 is an improper fraction, so convert it into a mixed fraction.

9/8 = 1 remainder = 1

The mixed fraction can be written as 1 1/8.

= 9 + 1 1/8

= 10 1/8

Therefore, 3\(\frac{5}{8}\) + 6\(\frac{1}{2}\) = 10 1/8.

Question 4.

1\(\frac{1}{12}\) + 4\(\frac{5}{12}\) = ____

Answer:

The above-given mixed fractions:

1 1/12 + 4 5/12

Here denominators are the same so we can add fractions directly.

= 1 + 4 + 1/12 + 5/12

= 5 + 6/12

= 5 + 1/2

* A mixed fraction a b/c can also be written as a + (b/c).

= 5 1/2

Therefore, 1\(\frac{1}{12}\) + 4\(\frac{5}{12}\) = 5 1/2.

Question 5.

11\(\frac{3}{5}\) + 6\(\frac{4}{15}\) = ____

Answer:

The above-given fractions:

11 3/5 + 6 4/15

= 11 + 6 + 3/5 + 4/15

= 17 + 3/5 + 4/15

Here the denominators are not the same. So we have to find the equivalent denominators.

– Find the common denominators:

15 is the least common multiple of denominators 5 and 15. Use it to convert to equivalent fractions with this common denominator.

= 17 + (9 + 4)/15

= 17 + 13/15

* A mixed fraction a b/c can also be written as a + (b/c).

= 17 13/15.

Therefore, 11\(\frac{3}{5}\) + 6\(\frac{4}{15}\) = 17 13/15.

Question 6.

9\(\frac{1}{2}\) + 12\(\frac{11}{20}\) = ____

Answer:

The above-given mixed fractions:

9 1/12 + 12 11/20

9 + 12 + 1/12 + 11/20

= 21 + 1/12 + 11/20

Here the denominators are not the same. So we have to find the equivalent denominators.

– Find the common denominators:

60 is the least common multiple of denominators 12 and 20. Use it to convert to equivalent fractions with this common denominator.

= 21 + (5 + 33)/60

= 21 + 38/60

38/60 is not simplified because 2 is a common factor of 38 and 60

38/60 is divided by 2 then we get 19/30

= 21 + 19/30

* A mixed fraction a b/c can also be written as a + (b/c).

= 21 19/30.

**Problem Solving**

Question 7.

A flower is 9\(\frac{3}{4}\) inçhes tall. In one week, it grew 1\(\frac{1}{8}\) inches. How tall is the flower at the end of the week? Write in simplest form.

Answer:

The above-given:

The number of inches is a flower tall = 9 3/4

The number of inches it grew = 1 1/8

The number of inches a flower is tall at the end of the week = x

x = 9 3/4 + 1 1/8

x = 9 + 1 + 3/4 + 1/8

x = 10 + 3/4 + 1/8

Here the denominators are not the same. So we have to find the equivalent denominators.

– Find the common denominators:

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

x = 10 + (6 + 1)/8

x = 10 + 7/8

x = 10 7/8

Therefore, a flower grows 10 7/8 inches at the end of the week.

Question 8.

Find ten and three-sevenths plus eighteen and two-sevenths. Write in words in simplest form.

Answer:

The above-given:

10 3/7 + 18 2/7

10 + 18 + 3/7 + 2/7

= 28 + 3/7 + 2/7

here the denominators are the same so we can directly add the fractions.

= 28 + 5/7

= 28 5/7.

In word form, we can write as twenty-eight and five-sevenths.

Question 9.

**Mathematical PRACTICE 6 Explain to a Friend** Connor is filling a 15-gallon wading pool. On his first trip, he carried 3\(\frac{1}{12}\)– gallons of water. He carried 3\(\frac{5}{6}\) gallons on his second trip and 3\(\frac{1}{2}\) gallons on his third trip. Suppose he carries 5 gallons on his next trip. Will the pool be filled? Explain.

Answer:

The above-given:

The number of gallons a wading pool = 15

The number of gallons of water he carried on the first trip = 3 1/12

The number of gallons of water he carried on the second trip = 3 5/6

The number of gallons of water he carried on the third trip = 3 1/12

if he carries 5 gallons on the fourth trip, is the pool filled = x

x = 3 1/12 + 3 5/6 + 3 1/12

x = 3 + 3 + 3 + 1/12 + 5/6 + 1/12

x = 9 + 2/12 + 5/6

x = 9 + 1/6 + 5/6 { 2/12 = 1/6 (divided by 2) }

Here the denominators are the same so we can add the fractions directly.

x = 9 + 6/6

x = 9 + 1

x = 10

up to three trips 10 gallons are carried by him.

On the next trip, he takes 5 gallons: 10 + 5 = 15 gallons.

Therefore, the warden pool is filled with 15 gallons of water.

**Test Practice**

Question 10.

Benjamin had 2\(\frac{1}{3}\) gallons of fruit punch left after a party. He had 1\(\frac{3}{4}\) gallons of lemonade left. How many total gallons did he have left?

A. 4\(\frac{1}{12}\) gallons

B. 3\(\frac{1}{12}\)– gallons

C. 1\(\frac{5}{12}\)– gallons

D. \(\frac{5}{12}\)– gallon

Answer: Option A is the correct answer.

Explanation:

The above-given:

The number of gallons of fruit punch left after a party = 2 1/3

The number of gallons of lemonade left = 1 3/4

The total number of gallons he left = x

x = 2 1/3 + 1 3/4

x = 2 + 1 + 1/3 + 3/4

x = 3 + 1/3 + 3/4

Here the denominators are not the same. So we have to find the equivalent denominators.

– Find the common denominators:

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

x = 3 + (4 + 9)/12

x = 3 + 13/12

13/12 is an improper fraction so convert it into a mixed fraction.

13/12 = 1 remainder = 1

The mixed fraction can be written as 1 1/12

x = 3 + 1 1/12

x = 4 1/12

Therefore, he left with 4 1/12 gallons.