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.