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McGraw-Hill Math Grade 7 Answer Key Lesson 8.4 Dividing Mixed Numbers
Exercises Divide
Question 1.
1\(\frac{1}{3}\) ÷ -2\(\frac{1}{2}\)
Answer:
–\(\frac{8}{15}\)
Explanation:
1\(\frac{1}{3}\) ÷ -2\(\frac{1}{2}\)
Convert mixed fraction into improper fraction.
\(\frac{4}{3}\) ÷ –\(\frac{5}{2}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{4}{3}\) x –\(\frac{2}{5}\)
Multiply the numerators and denominators,
4 x 2= 8
3 x 5 = 15
place the numerator over denominator,
–\(\frac{8}{15}\)
Question 2.
3\(\frac{3}{5}\) ÷ 1\(\frac{1}{8}\)
Answer:
3\(\frac{1}{5}\)
Explanation:
3\(\frac{3}{5}\) ÷ 1\(\frac{1}{8}\)
Convert mixed fraction into improper fraction.
\(\frac{18}{5}\) ÷ \(\frac{9}{8}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{18}{5}\) x \(\frac{8}{9}\)
Multiply the numerators and denominators,
18 x 8 = 2 x 8 = 16
5 x 9 = 5 = 5
place the numerator over denominator,
\(\frac{16}{5}\)
Reduce to the simplest form,
3\(\frac{1}{5}\)
Question 3.
7\(\frac{1}{7}\) ÷ 3\(\frac{1}{3}\)
Answer:
2\(\frac{1}{7}\)
Explanation:
7\(\frac{1}{7}\) ÷ 3\(\frac{1}{3}\)
Convert mixed fraction into improper fraction.
\(\frac{50}{7}\) ÷ \(\frac{10}{3}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{50}{7}\) x \(\frac{3}{10}\)
Multiply the numerators and denominators,
50 x 3 = 5 x 3 = 15
7 x 10 = 7 = 7
place the numerator over denominator,
\(\frac{15}{7}\)
Reduce to the simplest form,
2\(\frac{1}{7}\)
Question 4.
3\(\frac{4}{7}\) ÷ 2\(\frac{2}{5}\)
Answer:
1\(\frac{41}{84}\)
Explanation:
3\(\frac{4}{7}\) ÷ 2\(\frac{2}{5}\)
Convert mixed fraction into improper fraction.
\(\frac{25}{7}\) ÷ \(\frac{12}{5}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{25}{7}\) x \(\frac{5}{12}\)
Multiply the numerators and denominators,
25 x 5 = 125
7 x 12 = 84
place the numerator over denominator,
\(\frac{125}{84}\)
Reduce to the simplest form,
1\(\frac{41}{84}\)
Question 5.
6\(\frac{4}{5}\) ÷ 3\(\frac{2}{5}\)
Answer:
2
Explanation:
6\(\frac{4}{5}\) ÷ 3\(\frac{2}{5}\)
Convert mixed fraction into improper fraction.
\(\frac{34}{5}\) ÷ \(\frac{17}{5}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{34}{5}\) x \(\frac{5}{17}\)
Multiply the numerators and denominators,
34 x 5 = 2
5 x 17 = 1
place the numerator over denominator,
= \(\frac{2}{1}\) = 2
Question 6.
5\(\frac{1}{2}\) ÷ 3\(\frac{3}{4}\)
Answer:
1\(\frac{7}{15}\)
Explanation:
5\(\frac{1}{2}\) ÷ 3\(\frac{3}{4}\)
Convert mixed fraction into improper fraction.
\(\frac{11}{2}\) ÷ \(\frac{15}{4}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{11}{2}\) x \(\frac{4}{15}\)
Multiply the numerators and denominators,
11 x 4 = 11 x 2 = 22
2 x 15 = 15
place the numerator over denominator,
\(\frac{22}{15}\)
Reduce to the simplest form,
1\(\frac{7}{15}\)
Question 7.
4\(\frac{2}{9}\) ÷ 2\(\frac{4}{9}\)
Answer:
1\(\frac{8}{11}\)
Explanation:
4\(\frac{2}{9}\) ÷ 2\(\frac{4}{9}\)
Convert mixed fraction into improper fraction.
\(\frac{38}{9}\) ÷ \(\frac{22}{9}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{38}{9}\) x \(\frac{9}{22}\)
Multiply the numerators and denominators,
38 x 9 = 19
9 x 22 = 11
place the numerator over denominator,
\(\frac{19}{11}\)
Reduce to the simplest form,
1\(\frac{8}{11}\)
Question 8.
-9\(\frac{2}{7}\) ÷ -2\(\frac{1}{2}\)
Answer:
3\(\frac{5}{7}\)
Explanation:
-9\(\frac{2}{7}\) ÷ -2\(\frac{1}{2}\)
let – in numerator and – inn denominator get cancelled
Convert mixed fraction into improper fraction.
\(\frac{65}{7}\) ÷ \(\frac{5}{2}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{65}{7}\) x \(\frac{2}{5}\)
Multiply the numerators and denominators,
65 x 2 = 13 x 2 = 26
7 x 5 = 7
place the numerator over denominator,
\(\frac{26}{7}\)
Reduce to the simplest form,
3\(\frac{5}{7}\)
Question 9.
5\(\frac{6}{17}\) ÷ 2\(\frac{2}{3}\)
Answer:
2\(\frac{1}{136}\)
Explanation:
5\(\frac{6}{17}\) ÷ 2\(\frac{2}{3}\)
Convert mixed fraction into improper fraction.
\(\frac{91}{17}\) ÷ \(\frac{8}{3}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{91}{17}\) x \(\frac{3}{8}\)
Multiply the numerators and denominators,
91 x 3 = 273
17 x 8 = 136
place the numerator over denominator,
\(\frac{273}{136}\)
Reduce to the simplest form,
2\(\frac{1}{136}\)
Question 10.
5\(\frac{3}{13}\) ÷ 2\(\frac{3}{4}\)
Answer:
1\(\frac{129}{143}\)
Explanation:
5\(\frac{3}{13}\) ÷ 2\(\frac{3}{4}\)
Convert mixed fraction into improper fraction.
\(\frac{68}{13}\) ÷ \(\frac{11}{4}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{68}{13}\) x \(\frac{4}{11}\)
Multiply the numerators and denominators,
68 x 4 = 272
13 x 11 = 143
place the numerator over denominator,
\(\frac{272}{143}\)
Reduce to the simplest form,
1\(\frac{129}{143}\)
Question 11.
1\(\frac{3}{4}\) ÷ -4\(\frac{3}{5}\)
Answer:
–\(\frac{35}{92}\)
Explanation:
1\(\frac{3}{4}\) ÷ -4\(\frac{3}{5}\)
Convert mixed fraction into improper fraction.
\(\frac{7}{4}\) ÷ \(\frac{23}{5}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{7}{4}\) x \(\frac{5}{23}\)
Multiply the numerators and denominators,
7 x 5 = 35
4 x 23 = 92
place the numerator over denominator,
– \(\frac{35}{92}\)
Question 12.
9\(\frac{3}{8}\) ÷ 1\(\frac{1}{4}\)
Answer:
7\(\frac{1}{2}\)
Explanation:
9\(\frac{3}{8}\) ÷ 1\(\frac{1}{4}\)
Convert mixed fraction into improper fraction.
\(\frac{75}{8}\) ÷ \(\frac{5}{4}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{75}{8}\) x \(\frac{4}{5}\)
Multiply the numerators and denominators,
75 x 4 = 15
8 x 5 = 2
place the numerator over denominator,
\(\frac{15}{2}\)
Reduce to the simplest form,
7\(\frac{1}{2}\)
Question 13.
-44\(\frac{4}{5}\) ÷ -4\(\frac{1}{2}\)
Answer:
9\(\frac{43}{45}\)
Explanation:
-44\(\frac{4}{5}\) ÷ -4\(\frac{1}{2}\)
Convert mixed fraction into improper fraction.
\(\frac{224}{5}\) ÷ \(\frac{9}{2}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{224}{5}\) x \(\frac{2}{9}\)
Multiply the numerators and denominators,
224 x 2 = 448
5 x 9 = 45
place the numerator over denominator,
\(\frac{448}{45}\)
Reduce to the simplest form,
9\(\frac{43}{45}\)
Question 14.
1\(\frac{1}{2}\) ÷ 3\(\frac{1}{2}\)
Answer:
1\(\frac{129}{143}\)
Explanation:
1\(\frac{1}{2}\) ÷ 3\(\frac{1}{2}\)
Convert mixed fraction into improper fraction.
\(\frac{3}{2}\) ÷ \(\frac{7}{2}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{3}{2}\) x \(\frac{2}{7}\)
Multiply the numerators and denominators,
3 x 2 = 3
2 x 7 = 7
place the numerator over denominator,
\(\frac{3}{7}\)
Question 15.
5\(\frac{3}{5}\) ÷ 1\(\frac{1}{3}\)
Answer:
4\(\frac{1}{5}\)
Explanation:
5\(\frac{3}{5}\) ÷ 1\(\frac{1}{3}\)
Convert mixed fraction into improper fraction.
\(\frac{28}{5}\) ÷ \(\frac{4}{3}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{28}{5}\) x \(\frac{3}{4}\)
Multiply the numerators and denominators,
28 x 3 = 7 x 3 = 21
5 x 4 = 5
place the numerator over denominator,
\(\frac{21}{5}\)
Reduce to the simplest form,
4\(\frac{1}{5}\)
Question 16.
1\(\frac{2}{11}\) ÷ 3\(\frac{1}{3}\)
Answer:
\(\frac{39}{110}\)
Explanation:
1\(\frac{2}{11}\) ÷ 3\(\frac{1}{3}\)
Convert mixed fraction into improper fraction.
\(\frac{13}{11}\) ÷ \(\frac{10}{3}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{13}{11}\) x \(\frac{3}{10}\)
Multiply the numerators and denominators,
13 x 3 = 39
11 x 10 = 110
place the numerator over denominator,
\(\frac{39}{110}\)