McGraw Hill Math Grade 7 Lesson 6.7 Answer Key Subtracting Mixed Numbers with Unlike Denominators

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McGraw-Hill Math Grade 7 Answer Key Lesson 6.7 Subtracting Mixed Numbers with Unlike Denominators

Add Mixed Numbers

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

Question 2.
10\(\frac{3}{7}\) – 4\(\frac{2}{11}\)
Answer:
First subtract the whole numbers.
10 – 4 = 6
Second find a common denominator for the fractions.
\(\frac{3}{7}\) = \(\frac{33}{77}\)
\(\frac{2}{11}\) = \(\frac{14}{77}\) 
Third subtract the fractions.
\(\frac{33}{77}\) – \(\frac{14}{77}\) = \(\frac{19}{77}\) 
Fourth add the difference of the fractions to the difference of the whole numbers.
6 + \(\frac{19}{77}\) = 6\(\frac{19}{77}\) 

Question 3.
21\(\frac{5}{9}\) – 4\(\frac{2}{5}\)
Answer:
First subtract the whole numbers.
21 – 4 = 17
Second find a common denominator for the fractions.
\(\frac{5}{9}\) = \(\frac{25}{45}\)
\(\frac{2}{5}\) = \(\frac{18}{45}\) 
Third subtract the fractions.
\(\frac{25}{45}\) – \(\frac{18}{45}\) = \(\frac{7}{45}\) 
Fourth add the difference of the fractions to the difference of the whole numbers.
17 + \(\frac{7}{45}\) = 17\(\frac{7}{45}\) 

Question 4.
13\(\frac{5}{6}\) – 10\(\frac{2}{9}\)
Answer:
First subtract the whole numbers.
13 – 10 = 3
Second find a common denominator for the fractions.
\(\frac{5}{6}\) = \(\frac{15}{18}\)
\(\frac{2}{9}\) = \(\frac{4}{18}\) 
Third subtract the fractions.
\(\frac{15}{18}\) – \(\frac{4}{18}\) = \(\frac{11}{18}\) 
Fourth add the difference of the fractions to the difference of the whole numbers.
3 + \(\frac{11}{18}\) = 3\(\frac{11}{18}\) 

Question 5.
14\(\frac{2}{3}\) – 5\(\frac{1}{6}\)
Answer:
First subtract the whole numbers.
14 – 5 = 9
Second find a common denominator for the fractions.
\(\frac{2}{3}\) = \(\frac{4}{6}\) 
Third subtract the fractions.
\(\frac{4}{6}\) – \(\frac{1}{6}\) = \(\frac{3}{6}\) 
Fourth add the difference of the fractions to the difference of the whole numbers.
9 + \(\frac{3}{6}\) = 9\(\frac{3}{6}\) or 9\(\frac{1}{2}\)

Question 6.
21\(\frac{3}{4}\) – 11\(\frac{5}{9}\)
Answer:
First subtract the whole numbers.
21 – 11 = 10
Second find a common denominator for the fractions.
\(\frac{3}{4}\) = \(\frac{27}{36}\)
\(\frac{5}{9}\) = \(\frac{20}{36}\) 
Third subtract the fractions.
\(\frac{27}{36}\) – \(\frac{20}{36}\) = \(\frac{7}{36}\) 
Fourth add the difference of the fractions to the difference of the whole numbers.
10 + \(\frac{7}{36}\) = 10\(\frac{7}{36}\) 

Question 7.
13\(\frac{5}{6}\) – 3\(\frac{1}{7}\)
Answer:
First subtract the whole numbers.
13 – 3 = 10
Second find a common denominator for the fractions.
\(\frac{5}{6}\) = \(\frac{35}{42}\)
\(\frac{1}{7}\) = \(\frac{6}{42}\) 
Third subtract the fractions.
\(\frac{35}{42}\) – \(\frac{6}{42}\) = \(\frac{29}{42}\) 
Fourth add the difference of the fractions to the difference of the whole numbers.
10 + \(\frac{29}{42}\) = 10\(\frac{29}{42}\) 

Question 8.
43\(\frac{4}{5}\) – 29\(\frac{3}{11}\)
Answer:
First subtract the whole numbers.
43 – 29 = 14
Second find a common denominator for the fractions.
\(\frac{4}{5}\) = \(\frac{44}{55}\)
\(\frac{3}{11}\) = \(\frac{15}{55}\) 
Third subtract the fractions.
\(\frac{44}{55}\) – \(\frac{15}{55}\) = \(\frac{29}{55}\) 
Fourth add the difference of the fractions to the difference of the whole numbers.
14 + \(\frac{29}{55}\) = 14\(\frac{29}{55}\) 

Question 9.

Answer:

Explanation:
First subtract the whole numbers.
10 – 4 = 6
Second find a common denominator for the fractions.
\(\frac{6}{11}\) = \(\frac{12}{22}\)
\(\frac{1}{2}\) = \(\frac{11}{22}\) 
Third subtract the fractions.
\(\frac{12}{22}\) – \(\frac{11}{22}\) = \(\frac{1}{22}\) 
Fourth add the difference of the fractions to the difference of the whole numbers.
6 + \(\frac{1}{22}\) = 6\(\frac{1}{22}\) 

Question 10.

Answer:

Explanation:
First subtract the whole numbers.
13 – 11 = 2
Second find a common denominator for the fractions.
\(\frac{2}{3}\) = \(\frac{6}{9}\) 
Third subtract the fractions.
\(\frac{6}{9}\) – \(\frac{5}{9}\) = \(\frac{1}{9}\) 
Fourth add the difference of the fractions to the difference of the whole numbers.
2 + \(\frac{1}{9}\) = 2\(\frac{1}{9}\) 

Question 11.

Answer:

Explanation:
First subtract the whole numbers.
77 – 41 = 36
Second find a common denominator for the fractions.
\(\frac{2}{3}\) = \(\frac{34}{51}\)
\(\frac{2}{17}\) =\(\frac{6}{51}\) 
Third subtract the fractions.
\(\frac{34}{51}\) – \(\frac{6}{51}\) = \(\frac{28}{51}\) 
Fourth add the difference of the fractions to the difference of the whole numbers.
36 + \(\frac{28}{51}\) = 36\(\frac{28}{51}\) 

Question 12.

Answer:

Explanation:
First subtract the whole numbers.
19 – 3 = 16
Second find a common denominator for the fractions.
\(\frac{5}{7}\) = \(\frac{10}{14}\)  
Third subtract the fractions.
\(\frac{10}{14}\) – \(\frac{1}{14}\) = \(\frac{9}{14}\) 
Fourth add the difference of the fractions to the difference of the whole numbers.
16 + \(\frac{9}{14}\) = 16\(\frac{9}{14}\)

Question 13.
Janelle practiced playing the piano 2\(\frac{1}{2}\) hours on Saturday. On Sunday, she practiced for 3\(\frac{1}{4}\) hours. How many more hours did Janelle practice on Sunday than on Saturday?
Answer:

Question 14.
Robby is helping his father make a casserole for dinner. They purchased 1\(\frac{1}{4}\) pounds of potatoes, and used \(\frac{2}{3}\) pounds of potatoes to make one casserole.
Do they have enough potatoes left over to make the casserole a second time?
Answer: