McGraw Hill Math Grade 7 Lesson 6.6 Answer Key Adding Mixed Numbers with Unlike Denominators

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McGraw-Hill Math Grade 7 Answer Key Lesson 6.6 Adding Mixed Numbers with Unlike Denominators

Add Mixed Numbers

Question 1.
2\(\frac{1}{2}\) + 3\(\frac{1}{4}\)
Answer:
First add the whole numbers.
2 + 3 = 5
Second find a common denominator for the fractions.
\(\frac{1}{2}\) = \(\frac{2}{4}\)
Third add the fractions.
\(\frac{2}{4}\) + \(\frac{1}{4}\) = \(\frac{3}{4}\)
Fourth add the sum of the fractions to the sum of the whole numbers.
2\(\frac{1}{2}\) + 3\(\frac{1}{4}\) = 5 + \(\frac{3}{4}\) = 5\(\frac{3}{4}\)

Question 2.
3\(\frac{2}{3}\) + 4\(\frac{3}{7}\)
Answer:
First add the whole numbers.
3 + 4 = 7
Second find a common denominator for the fractions.
\(\frac{2}{3}\) = \(\frac{14}{21}\)
\(\frac{3}{7}\) = \(\frac{9}{21}\)
Third add the fractions.
\(\frac{14}{21}\) + \(\frac{9}{21}\) = \(\frac{23}{21}\) = 1\(\frac{2}{21}\)
Fourth add the sum of the fractions to the sum of the whole numbers.
3\(\frac{2}{3}\) + 4\(\frac{3}{7}\) = 7 + 1\(\frac{2}{21}\) = 8\(\frac{2}{21}\)

Question 3.
4\(\frac{5}{6}\) + 7\(\frac{3}{4}\)
Answer:
First add the whole numbers.
4 + 7 = 11
Second find a common denominator for the fractions.
\(\frac{5}{6}\) = \(\frac{10}{12}\)
\(\frac{3}{4}\) = \(\frac{9}{12}\)
Third add the fractions.
\(\frac{10}{12}\) + \(\frac{9}{12}\) = \(\frac{19}{12}\) = 1\(\frac{7}{12}\)
Fourth add the sum of the fractions to the sum of the whole numbers.
4\(\frac{5}{6}\) + 7\(\frac{3}{4}\) = 11 + 1\(\frac{7}{12}\) = 12\(\frac{7}{12}\)

Question 4.
3\(\frac{3}{4}\) + 2\(\frac{1}{3}\)
Answer:
First add the whole numbers.
3 + 2 = 5
Second find a common denominator for the fractions.
\(\frac{3}{4}\) = \(\frac{9}{12}\)
\(\frac{1}{3}\) = \(\frac{4}{12}\)
Third add the fractions.
\(\frac{9}{12}\) + \(\frac{4}{12}\) = \(\frac{13}{12}\) = 1\(\frac{1}{12}\)
Fourth add the sum of the fractions to the sum of the whole numbers.
3\(\frac{3}{4}\) + 2\(\frac{1}{3}\) = 5 + 1\(\frac{1}{12}\) = 6\(\frac{1}{12}\)

Question 5.
9\(\frac{1}{2}\) + 4\(\frac{1}{5}\)
Answer:
First add the whole numbers.
9 + 4 = 13
Second find a common denominator for the fractions.
\(\frac{1}{2}\) = \(\frac{5}{10}\)
\(\frac{1}{5}\) = \(\frac{2}{10}\)
Third add the fractions.
\(\frac{5}{10}\) + \(\frac{2}{10}\) = \(\frac{7}{10}\) 
Fourth add the sum of the fractions to the sum of the whole numbers.
9\(\frac{1}{2}\) + 4\(\frac{1}{5}\) = 13 + \(\frac{7}{10}\) = 13\(\frac{7}{10}\)

Question 6.
54\(\frac{1}{2}\) + 14\(\frac{2}{3}\)
Answer:
First add the whole numbers.
54 + 14 = 68
Second find a common denominator for the fractions.
\(\frac{1}{2}\) = \(\frac{3}{6}\)
\(\frac{2}{3}\) = \(\frac{4}{6}\)
Third add the fractions.
\(\frac{3}{6}\) + \(\frac{4}{6}\) = \(\frac{7}{6}\) = 1 \(\frac{1}{6}\)
Fourth add the sum of the fractions to the sum of the whole numbers.
54\(\frac{1}{2}\) + 14\(\frac{2}{3}\) = 68 + 1\(\frac{1}{6}\) = 69\(\frac{1}{6}\)

Question 7.
10\(\frac{5}{7}\) + 12\(\frac{2}{3}\)
Answer:
First add the whole numbers.
10 + 12 = 22
Second find a common denominator for the fractions.
\(\frac{5}{7}\) = \(\frac{15}{21}\)
\(\frac{2}{3}\) = \(\frac{14}{21}\)
Third add the fractions.
\(\frac{15}{21}\) + \(\frac{14}{21}\) = \(\frac{29}{21}\) = 1\(\frac{8}{21}\)
Fourth add the sum of the fractions to the sum of the whole numbers.
10\(\frac{5}{7}\) + 12\(\frac{2}{3}\) = 22 + 1\(\frac{8}{21}\) = 23\(\frac{8}{21}\)

Question 8.
4\(\frac{2}{9}\) + 3\(\frac{2}{7}\)
Answer:
First add the whole numbers.
4 + 3 = 7
Second find a common denominator for the fractions.
\(\frac{2}{9}\) = \(\frac{14}{63}\)
\(\frac{2}{7}\) = \(\frac{18}{63}\)
Third add the fractions.
\(\frac{14}{63}\) + \(\frac{18}{63}\) = \(\frac{32}{63}\) 
Fourth add the sum of the fractions to the sum of the whole numbers.
4\(\frac{2}{9}\) + 3\(\frac{2}{7}\) = 7 + \(\frac{31}{63}\) = 7\(\frac{32}{63}\)

Question 9.
13\(\frac{4}{5}\) + 4\(\frac{3}{11}\)
Answer:
First add the whole numbers.
13 + 4 = 17
Second find a common denominator for the fractions.
\(\frac{4}{5}\) = \(\frac{44}{55}\)
\(\frac{3}{11}\) = \(\frac{15}{55}\)
Third add the fractions.
\(\frac{44}{55}\) + \(\frac{15}{55}\) = \(\frac{59}{55}\) = 1\(\frac{4}{55}\)
Fourth add the sum of the fractions to the sum of the whole numbers.
13\(\frac{4}{5}\) + 4\(\frac{3}{11}\) = 17 + 1\(\frac{4}{55}\) = 18\(\frac{4}{55}\)

Question 10.
23\(\frac{1}{6}\) + 57\(\frac{3}{13}\)
Answer:
First add the whole numbers.
23 + 57 = 80
Second find a common denominator for the fractions.
\(\frac{1}{6}\) = \(\frac{13}{78}\)
\(\frac{3}{13}\) = \(\frac{18}{78}\)
Third add the fractions.
\(\frac{13}{78}\) + \(\frac{18}{78}\) = \(\frac{31}{78}\) 
Fourth add the sum of the fractions to the sum of the whole numbers.
23\(\frac{1}{6}\) + 57\(\frac{3}{13}\) = 80 + \(\frac{31}{78}\) = 80\(\frac{31}{78}\)

Question 11.
22\(\frac{3}{11}\) + 14\(\frac{2}{5}\)
Answer:
First add the whole numbers.
22 + 14 = 36
Second find a common denominator for the fractions.
\(\frac{3}{11}\) = \(\frac{15}{55}\)
\(\frac{2}{5}\) = \(\frac{22}{55}\)
Third add the fractions.
\(\frac{15}{55}\) + \(\frac{22}{55}\) = \(\frac{37}{55}\) 
Fourth add the sum of the fractions to the sum of the whole numbers.
22\(\frac{3}{11}\) + 14\(\frac{2}{5}\) = 36 + \(\frac{37}{55}\) = 36\(\frac{37}{55}\)

Question 12.
4\(\frac{5}{7}\) + 3\(\frac{1}{3}\)
Answer:
First add the whole numbers.
4 + 3 = 7
Second find a common denominator for the fractions.
\(\frac{5}{7}\) = \(\frac{15}{21}\)
\(\frac{1}{3}\) = \(\frac{7}{21}\)
Third add the fractions.
\(\frac{15}{21}\) + \(\frac{7}{21}\) = \(\frac{22}{21}\) = 1\(\frac{1}{21}\)
Fourth add the sum of the fractions to the sum of the whole numbers.
4\(\frac{5}{7}\) + 3\(\frac{1}{3}\) = 7 + 1\(\frac{1}{21}\) = 8\(\frac{1}{21}\)

Question 13.

Answer:

Explanation:
First add the whole numbers.
5 + 7 = 12
Second find a common denominator for the fractions.
\(\frac{1}{4}\) = \(\frac{15}{60}\)
\(\frac{2}{15}\) = \(\frac{8}{60}\)
Third add the fractions.
\(\frac{15}{60}\) + \(\frac{8}{60}\) = \(\frac{23}{60}\) 
Fourth add the sum of the fractions to the sum of the whole numbers.
5\(\frac{1}{4}\) + 7\(\frac{2}{15}\) = 12 + \(\frac{23}{60}\) = 12\(\frac{23}{60}\)

Question 14.

Answer:

Explanation:
First add the whole numbers.
102 + 355 = 457
Second find a common denominator for the fractions.
\(\frac{5}{6}\) = \(\frac{55}{66}\)
\(\frac{1}{11}\) = \(\frac{6}{66}\)
Third add the fractions.
\(\frac{55}{66}\) + \(\frac{6}{66}\) = \(\frac{61}{66}\) 
Fourth add the sum of the fractions to the sum of the whole numbers.
102\(\frac{5}{6}\) + 355\(\frac{1}{11}\) = 457 + \(\frac{61}{66}\) = 457\(\frac{61}{66}\)

Question 15.

Answer:

Explanation:
First add the whole numbers.
56 + 89 = 145
Second find a common denominator for the fractions.
\(\frac{1}{3}\) = \(\frac{14}{42}\)
\(\frac{5}{14}\) = \(\frac{15}{42}\)
Third add the fractions.
\(\frac{14}{42}\) + \(\frac{15}{42}\) = \(\frac{29}{42}\) 
Fourth add the sum of the fractions to the sum of the whole numbers.
56\(\frac{1}{3}\) + 89\(\frac{5}{14}\) = 145 + \(\frac{29}{42}\) = 145\(\frac{29}{42}\)

Question 16.

Answer:

First add the whole numbers.
21 + 122 = 143
Second find a common denominator for the fractions.
\(\frac{1}{2}\) = \(\frac{4}{8}\)
Third add the fractions.
\(\frac{4}{8}\) + \(\frac{3}{8}\) = \(\frac{7}{8}\) 
Fourth add the sum of the fractions to the sum of the whole numbers.
21\(\frac{1}{2}\) + 122\(\frac{3}{8}\) = 143 + \(\frac{7}{8}\) = 143\(\frac{7}{8}\)