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McGraw-Hill Math Grade 7 Answer Key Lesson 8.3 Dividing Fractions by Fractions
Exercises Divide
Question 1.
\(\frac{5}{7}\) ÷ \(\frac{3}{4}\)
Answer:
\(\frac{20}{21}\)
Explanation:
\(\frac{5}{7}\) ÷ \(\frac{3}{4}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{5}{7}\) x \(\frac{4}{3}\)
Multiply the numerators and denominators,
4 x 5 = 20
3 x 7 = 21
place the numerator over denominator,
\(\frac{20}{21}\)
Question 2.
\(\frac{2}{3}\) ÷ \(\frac{2}{7}\)
Answer:
2\(\frac{1}{3}\)
Explanation:
\(\frac{2}{3}\) ÷ \(\frac{2}{7}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{2}{3}\) x \(\frac{7}{2}\)
Multiply the numerators and denominators,
2 x 7 = 14
3 x 2 = 6
place the numerator over denominator,
\(\frac{14}{6}\)
Reduce to the simplest form,
\(\frac{7}{3}\) = 2\(\frac{1}{3}\)
Question 3.
\(\frac{1}{9}\) ÷ –\(\frac{3}{7}\)
Answer:-
–\(\frac{7}{27}\)
Explanation:
\(\frac{1}{9}\) ÷ –\(\frac{3}{7}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{1}{9}\) x –\(\frac{7}{3}\)
Multiply the numerators and denominators,
1 x 7 = 7
3 x 9 = 27
place the numerator over denominator,
–\(\frac{7}{27}\)
Question 4.
\(\frac{3}{4}\) ÷ \(\frac{1}{9}\)
Answer:
6\(\frac{3}{4}\)
Explanation:
\(\frac{3}{4}\) ÷ \(\frac{1}{9}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{3 X 9}{4}\)
\(\frac{27}{4}\)
Reduce to the simplest form,
6\(\frac{3}{4}\)
Question 5.
–\(\frac{3}{13}\) ÷ –\(\frac{2}{9}\)
Answer:
1\(\frac{1}{26}\)
Explanation:
–\(\frac{3}{13}\) ÷ –\(\frac{2}{9}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{3}{13}\) x \(\frac{9}{2}\)
Multiply the numerators and denominators,
3 x 9 = 27
13 x 2 = 26
place the numerator over denominator,
\(\frac{27}{26}\)
Reduce to the simplest form,
1\(\frac{1}{26}\)
Question 6.
\(\frac{1}{9}\) ÷ \(\frac{1}{3}\)
Answer:
\(\frac{1}{3}\)
Explanation:
\(\frac{1}{9}\) ÷ \(\frac{1}{3}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{1 X 3}{9}\)
\(\frac{1}{3}\)
Question 7.
\(\frac{2}{13}\) ÷ \(\frac{1}{5}\)
Answer:
\(\frac{10}{13}\)
Explanation:
\(\frac{2}{13}\) ÷ \(\frac{1}{5}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{2 X 5}{13}\)
\(\frac{10}{13}\)
Question 8.
\(\frac{3}{13}\) ÷ \(\frac{2}{13}\)
Answer:
1\(\frac{1}{2}\)
Explanation:
\(\frac{3}{13}\) ÷ \(\frac{2}{13}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{3}{13}\) x \(\frac{13}{2}\)
Multiply the numerators and denominators,
3 x 13 = 39
13 x 2 = 26
place the numerator over denominator,
\(\frac{39}{26}\)
Reduce to the simplest form,
\(\frac{3}{2}\) = 1\(\frac{1}{2}\)
Question 9.
\(\frac{4}{3}\) ÷ \(\frac{1}{4}\)
Answer:
5\(\frac{1}{3}\)
Explanation:
\(\frac{4}{3}\) ÷ \(\frac{1}{4}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{4 X 4}{3}\)
\(\frac{16}{3}\)
Reduce to the simplest form,
5\(\frac{1}{3}\)
Question 10.
\(\frac{15}{4}\) ÷ \(\frac{4}{3}\)
Answer:
2\(\frac{13}{16}\)
Explanation:
\(\frac{15}{4}\) ÷ \(\frac{4}{3}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{15}{4}\) x \(\frac{3}{4}\)
Multiply the numerators and denominators,
15 x 3 = 45
4 x 4 = 16
place the numerator over denominator,
\(\frac{45}{16}\)
Reduce to the simplest form,
2\(\frac{13}{16}\)
Question 11.
\(\frac{6}{7}\) ÷ \(\frac{1}{7}\)
Answer:
6
Explanation:
\(\frac{6}{7}\) ÷ \(\frac{1}{7}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{6 X 7}{7}\)
\(\frac{42}{7}\) = 6
Question 12.
\(\frac{3}{17}\) ÷ –\(\frac{4}{17}\)
Answer:
–\(\frac{3}{4}\)
Explanation:
\(\frac{3}{17}\) ÷ –\(\frac{4}{17}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{3}{17}\) x –\(\frac{17}{4}\)
Multiply the numerators and denominators,
3 x 17 = 51
17 x 4 = 68
place the numerator over denominator,
–\(\frac{51}{68}\)
Reduce to the simplest form,
–\(\frac{3}{4}\)
Question 13.
\(\frac{1}{11}\) ÷ \(\frac{22}{3}\)
Answer:
\(\frac{3}{242}\)
Explanation:
\(\frac{1}{11}\) ÷ \(\frac{22}{3}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{3}{22 X11}\)
\(\frac{3}{242}\)
Question 14.
–\(\frac{3}{7}\) ÷ –\(\frac{1}{21}\)
Answer:
9
Explanation:
–\(\frac{3}{7}\) ÷ –\(\frac{1}{21}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{3 X 21}{7}\)
\(\frac{63}{7}\) = 9
Question 15.
\(\frac{5}{14}\) ÷ \(\frac{1}{7}\)
Answer:
2\(\frac{1}{2}\)
Explanation:
\(\frac{5}{14}\) ÷ \(\frac{1}{7}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{5 X 7}{14}\)
\(\frac{35}{14}\)
Reduce to the simplest form,
\(\frac{5}{2}\) = 2\(\frac{1}{2}\)
Question 16.
\(\frac{3}{4}\) ÷ \(\frac{8}{3}\)
Answer:
\(\frac{9}{32}\)
Explanation:
\(\frac{3}{4}\) ÷ \(\frac{8}{3}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{3}{4}\) x \(\frac{3}{8}\)
Multiply the numerators and denominators,
3 x 3 = 9
4 x 8 = 32
place the numerator over denominator,
\(\frac{9}{32}\)