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.

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.

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. $$\frac{4}{3}$$ + $$\frac{7}{3}$$ = $$\frac{4+7}{3}$$ = 3. Simplify. Write the improper fraction as a mixed number. The model shows 11 divided into groups of 3. 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 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 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$$\frac{2}{4}$$ = _______________
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$$\frac{1}{6}$$ = ________________
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$$\frac{2}{5}$$ = ________________
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$$\frac{2}{6}$$ = ________________
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$$\frac{1}{4}$$ = ________________
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$$\frac{3}{8}$$ = _________________
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$$\frac{3}{10}$$ = ________________
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$$\frac{1}{10}$$ = __________________
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?
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?
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?
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
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.

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