All the solutions provided in **McGraw Hill My Math Grade 4 Answer Key PDF Chapter 9 Lesson 6 Add Mixed Numbers **will give you a clear idea of the concepts.

## McGraw-Hill My Math Grade 4 Answer Key Chapter 9 Lesson 6 Add Mixed Numbers

Mixed numbers are numbers with a whole number and a fraction. You can decompose mixed numbers to add them. Use the Associative Property to group the whole numbers and like fractions together.

**Math in My World
**

**Example 1**

Madison made a fruit salad. She used 3\(\frac{1}{4}\) cups of strawberries and 2\(\frac{1}{4}\) cups of blueberries. How many cups of berries did Madison use altogether?

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

Decompose each mixed number as a sum of whole numbers and unit fractions.

So, Madison used cups of berries.

Answer:

Number of cups of berries did Madison use altogether = \(\frac{11}{2}\) or

Explanation:

Number of cups of strawberries she used = 3\(\frac{1}{4}\)

Number of cups of blueberries she used = 2\(\frac{1}{4}\)

Number of cups of berries did Madison use altogether = Number of cups of strawberries she used + Number of cups of blueberries she used

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

= {[(3 × 4) + 1] ÷ 4} + {[(2 × 4) + 1] ÷ 4}

= [(12 + 1) ÷ 4] + [(8 + 1) ÷ 4]

= \(\frac{13}{4}\) + \(\frac{9}{4}\)

= (13 + 9) ÷ 4

= \(\frac{22}{4}\) ÷ \(\frac{2}{2}\)

= \(\frac{11}{2}\) or 5\(\frac{1}{2}\)

**Example 2**

Find 1\(\frac{1}{3}\) + 2\(\frac{1}{3}\).

1. Write each mixed number as an equivalent improper fraction.

2. Add like fractions.

\(\frac{4}{3}\) + \(\frac{7}{3}\) = \(\frac{4+7}{3}\) =

3. Simplify. Write the improper fraction as a mixed number. The model shows 11 divided into groups of 3.

Answer:

Sum of 1\(\frac{1}{3}\) and 2\(\frac{1}{3}\), we get \(\frac{11}{3}\) or 3\(\frac{2}{3}\)

Explanation:

Sum of mixed fractions:

1\(\frac{1}{3}\) + 2\(\frac{1}{3}\)

= {[(1 × 3) + 1] ÷ 3} + {[(2 × 3) + 1] ÷ 3}

= [(3 + 1) ÷ 3] + [(6 + 1) ÷ 3]

= \(\frac{4}{3}\) + \(\frac{7}{3}\)

= [(4 + 7) ÷ 3]

= \(\frac{11}{3}\) or 3\(\frac{2}{3}\)

**Talk Math
**Explain how adding mixed numbers is different than adding whole numbers.

Answer:

Adding mixed fractions means finding the sum of mixed fractions where as adding whole numbers means adding numbers directly.

Explanation:

A mixed number is a whole number, and a proper fraction represented together. It generally represents a number between any two whole numbers.

The numbers that include natural numbers and zero are called whole numbers.

**Guided Practice
**Question 1.

Find the sum. Write in simplest form.

2\(\frac{3}{6}\) + 2\(\frac{1}{6}\) = ___________ + ____________ + \(\frac{3}{6}\) + ___________ + _____________ + \(\frac{1}{6}\)

= (__________ + ___________ + ___________ + _____________) + (\(\frac{3}{6}\) + \(\frac{1}{6}\))

= 4 + , or

Answer:

Sum of 2\(\frac{3}{6}\) and 2\(\frac{1}{6}\), we get

Explanation:

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

2\(\frac{1}{6}\) = 1 + 1 + \(\frac{1}{6}\)

Sum of 2\(\frac{3}{6}\) and 2\(\frac{1}{6}\) = 1 + 1 + \(\frac{3}{6}\) + 1 + 1 + \(\frac{1}{6}\)

= 4 + \(\frac{3}{6}\) + \(\frac{1}{6}\)

= 4 + [(3 + 1) ÷ 6]

= 4 + \(\frac{4}{6}\)

= 4\(\frac{4}{6}\)

### McGraw Hill My Math Grade 4 Chapter 9 Lesson 6 My Homework Answer Key

**Practice
**

**Find each sum. Write in simplest form.**

Question 1.

4\(\frac{1}{4}\) + 2\(\frac{2}{4}\) = _______________

Answer:

Sum of 4\(\frac{1}{4}\) and 2\(\frac{2}{4}\), we get \(\frac{27}{4}\) or 6\(\frac{3}{4}\)

Explanation:

Sum:

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

= {[(4 × 4) + 1] ÷ 4} + {[(2 × 4) + 2] ÷ 4}

= [(16 + 1) ÷ 4] + [(8 + 2) ÷ 4]

= (17 ÷ 4) + (10 ÷ 4)

= (17 + 10) ÷ 4

= \(\frac{27}{4}\) or 6\(\frac{3}{4}\)

Question 2.

3\(\frac{3}{6}\) + 6\(\frac{1}{6}\) = ________________

Answer:

Sum of 3\(\frac{3}{6}\) and 6\(\frac{1}{6}\), we get \(\frac{29}{3}\) or 9\(\frac{2}{6}\)

Explanation:

Sum of 3\(\frac{3}{6}\) + 6\(\frac{1}{6}\):

3\(\frac{3}{6}\) + 6\(\frac{1}{6}\)

= {[(3 × 6) + 3] ÷ 6} + {[(6 × 6) + 1] ÷ 6}

= [(18 + 3) ÷ 6] + [(36 + 1) ÷ 6]

= \(\frac{21}{6}\) + \(\frac{37}{6}\)

= [(21 + 37) ÷ 6]

= \(\frac{58}{6}\) ÷ \(\frac{2}{2}\)

= \(\frac{29}{3}\) or 9\(\frac{2}{6}\)

Question 3.

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

Answer:

Sum of 6\(\frac{2}{5}\) and 3\(\frac{2}{5}\), we get \(\frac{49}{5}\) or 9\(\frac{4}{5}\)

Explanation:

Sum:

6\(\frac{2}{5}\) + 3\(\frac{2}{5}\)

= {[(6 × 5) + 2] ÷ 5} + {[(3 × 5) + 2] ÷ 5}

= [(30 + 2) ÷ 5] + [(15 + 2) ÷ 5]

= \(\frac{32}{5}\) + \(\frac{17}{5}\)

= [(32 + 17) ÷ 5]

= \(\frac{49}{5}\) or 9\(\frac{4}{5}\)

Question 4.

4\(\frac{1}{6}\) + 1\(\frac{2}{6}\) = ________________

Answer:

Sum of 4\(\frac{1}{6}\) and 1\(\frac{2}{6}\), we get \(\frac{17}{3}\) or 5\(\frac{2}{3}\)

Explanation:

Sum:

4\(\frac{1}{6}\) + 1\(\frac{2}{6}\)

= {[(4 × 6) + 1] ÷ 6} + {[(1 × 6) + 2] ÷ 6}

= [(24 + 1) ÷ 6] + [(7 + 2) ÷ 6]

= \(\frac{25}{6}\) + \(\frac{9}{6}\)

= [(25 + 9) ÷ 6]

= \(\frac{34}{6}\) ÷ \(\frac{2}{2}\)

= \(\frac{17}{3}\) or 5\(\frac{2}{3}\)

Question 5.

2\(\frac{1}{4}\) + 9\(\frac{1}{4}\) = ________________

Answer:

Sum of 2\(\frac{1}{4}\) and 9\(\frac{1}{4}\), we get \(\frac{23}{2}\) or 11\(\frac{1}{2}\)

Explanation:

Sum:

2\(\frac{1}{4}\) + 9\(\frac{1}{4}\)

= {[(2 × 4) + 1] ÷ 4} + {[(9 × 4) + 1] ÷ 4}

= [(8 + 1) ÷ 4] + [(36 + 1) ÷ 4]

= \(\frac{9}{4}\) + \(\frac{37}{4}\)

= [(9 + 37) ÷ 4]

= \(\frac{46}{4}\) ÷ \(\frac{2}{2}\)

= \(\frac{23}{2}\) or 11\(\frac{1}{2}\)

Question 6.

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

Answer:

Sum of 7\(\frac{4}{8}\) and 1\(\frac{3}{8}\), we get \(\frac{71}{8}\) or 8\(\frac{7}{8}\)

Explanation:

Sum:

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

= {[(7 × 8) + 4] ÷ 8} + {[(1 × 8) + 3] ÷ 8}

= [(56 + 4) ÷ 8] + [(8 + 3) ÷ 8]

= \(\frac{60}{8}\) + \(\frac{11}{8}\)

= [(60 + 11) ÷ 8]

= \(\frac{71}{8}\) or 8\(\frac{7}{8}\)

Question 7.

5\(\frac{6}{10}\) + 8\(\frac{3}{10}\) = ________________

Answer:

Sum of 5\(\frac{6}{10}\) and 8\(\frac{3}{10}\), we get \(\frac{139}{10}\) or 13\(\frac{9}{10}\)

Explanation:

Sum:

5\(\frac{6}{10}\) + 8\(\frac{3}{10}\)

= {[(5 × 10) + 6] ÷ 10} + {[(8 × 10) + 3] ÷ 10}

= [(50 + 6) ÷ 10] + [(80 + 3) ÷ 10]

= \(\frac{56}{10}\) + \(\frac{83}{10}\)

= [(56 + 83) ÷ 10]

= \(\frac{139}{10}\) or 13\(\frac{9}{10}\)

Question 8.

12\(\frac{5}{10}\) + 6\(\frac{1}{10}\) = __________________

Answer:

Sum of 12\(\frac{5}{10}\) and 6\(\frac{1}{10}\), we get \(\frac{93}{5}\) or 18\(\frac{3}{10}\)

Explanation:

Sum:

12\(\frac{5}{10}\) + 6\(\frac{1}{10}\)

= {[(12 × 10) + 5] ÷ 10} + {[(6 × 10) + 1] ÷ 10}

= [(120 + 5) ÷ 10] + [(60 + 1) ÷ 10]

= \(\frac{125}{10}\) + \(\frac{61}{10}\)

= [(125 + 61) ÷ 10]

= \(\frac{186}{10}\) ÷ \(\frac{2}{2}\)

= \(\frac{93}{5}\) or 18\(\frac{3}{10}\)

**Problem Solving
**

**Solve. Write the answer in simplest form.**

Question 9.

James cut 1\(\frac{1}{4}\) dozen flowers for a bouquet. Gwen added 1\(\frac{2}{4}\) dozen flowers to the bouquet. How many dozen flowers are there altogether?

Answer:

Number of dozen flowers are there altogether = \(\frac{11}{4}\)

Explanation:

Number of dozen flowers for a bouquet James cut = 1\(\frac{1}{4}\)

Number of dozen flowers for a bouquet Gwen added = 1\(\frac{2}{4}\)

Number of dozen flowers are there altogether = Number of dozen flowers for a bouquet James cut + Number of dozen flowers for a bouquet Gwen added

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

= {[(1 × 4) + 1] ÷ 4} + {[(1 × 4) + 2] ÷ 4}

= [(4 + 1) ÷ 4] + [(4 + 2) ÷ 4]

= \(\frac{5}{4}\) + \(\frac{6}{4}\)

= (5 + 6) ÷ 4

= \(\frac{11}{4}\)

Question 10.

On Monday, Simon’s class filled 3\(\frac{2}{5}\) boxes with books to donate to charity. On Wednesday, the class filled 4\(\frac{2}{5}\) more boxes with books to donate. How many boxes of books will Simon’s class donate in all?

Answer:

Number of boxes of books Simon’s class donate in all = \(\frac{39}{5}\)

Explanation:

Number of boxes with books to donate to charity Simon’s class filled On Monday = 3\(\frac{2}{5}\)

Number of more boxes with books to donate to charity Simon’s class filled On Wednesday = 4\(\frac{2}{5}\)

Number of boxes of books Simon’s class donate in all = Number of more boxes with books to donate to charity Simon’s class filled On Wednesday + Number of boxes with books to donate to charity Simon’s class filled

= 4\(\frac{2}{5}\) – 3\(\frac{2}{5}\)

= {[(4 × 5) + 2] ÷ 5} + {[(3 × 5) + 2] ÷ 5}

= [(20 + 2) ÷ 5] + [(15 + 2) ÷ 5]

= (22 ÷ 5) + (17 ÷ 5)

= (22 + 17) ÷ 5

= \(\frac{39}{5}\)

Question 11.

**Mathematical PRACTICE** Use Number Sense Marissa rode her bike to the park and back home. She lives 2\(\frac{3}{10}\) miles from the park. How many miles did Marissa ride her bike in all?

Answer:

Number of miles Marissa ride her bike in all = \(\frac{23}{5}\)

Explanation:

Number of miles from the park she lives = 2\(\frac{3}{10}\)

Marissa rode her bike to the park and back home.

=> Number of miles Marissa ride her bike in all = 2 × Number of miles from the park she lives

=> 2 × 2\(\frac{3}{10}\)

=> 2 × {[(2 × 10) + 3] ÷ 10}

=> 2 × \(\frac{23}{10}\)

=> 1 × \(\frac{23}{5}\)

=> \(\frac{23}{5}\)

**Test Practice
**Question 12.

Nate is 10\(\frac{9}{12}\) years old. How old will he be in 2\(\frac{1}{12}\) more years?

(A) 13\(\frac{1}{3}\) years old

(B) 12\(\frac{5}{6}\) years old

(C) 12\(\frac{1}{4}\) years old

(D) 12\(\frac{3}{12}\) years old

Answer:

Future age of Nate = 12\(\frac{5}{6}\) years old.

(B) 12\(\frac{5}{6}\) years old

Explanation:

Present age of Nate = 10\(\frac{9}{12}\) years.

Future age of Nate = 2\(\frac{1}{12}\) + Present age of Nate

= 2\(\frac{1}{12}\) + 10\(\frac{9}{12}\)

= {[(2 × 12) + 1] ÷ 12} + {[(10 × 12) + 9] ÷ 12}

= [(24 + 1) ÷ 12] + [(120 + 9) ÷ 12]

= (25 ÷ 12) + (129 ÷ 12)

= (25 + 129) ÷ 12

= 154 ÷ 12

= \(\frac{154}{12}\) ÷ \(\frac{2}{2}\)

= \(\frac{77}{6}\)

= 12\(\frac{5}{6}\) years.