Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 5.4 Dividing Mixed Numbers to secure good marks & knowledge in the exams.
McGraw-Hill Math Grade 8 Answer Key Lesson 5.4 Dividing Mixed Numbers
Exercises Divide
Question 1.
3\(\frac{1}{6}\) ÷ 2\(\frac{1}{3}\)
Answer:
\(\frac{19}{14}\),
Explanation:
3\(\frac{1}{6}\) ÷ 2\(\frac{1}{3}\)
= \(\frac{18 + 1}{6}\) ÷ \(\frac{6 + 1}{3}\)
= \(\frac{19}{6}\) ÷ \(\frac{7}{3}\)
= \(\frac{19}{6}\) x \(\frac{3}{7}\)
= \(\frac{19 X 3}{6 X 7}\)
= \(\frac{19}{14}\)
Question 2.
4\(\frac{3}{7}\) ÷ 3\(\frac{3}{8}\)
Answer:
1\(\frac{59}{189}\),
Explanation:
4\(\frac{3}{7}\) ÷ 3\(\frac{3}{8}\)
= \(\frac{28 + 3}{7}\) ÷ \(\frac{24 + 3}{8}\)
= \(\frac{31}{7}\) ÷ \(\frac{27}{8}\)
= \(\frac{31}{7}\) x \(\frac{8}{27}\)
= \(\frac{31 X 8}{7 X 27}\)
= \(\frac{248}{189}\)
= 1\(\frac{59}{189}\)
Question 3.
5\(\frac{3}{7}\) ÷ 2\(\frac{2}{3}\)
Answer:
2\(\frac{1}{28}\),
Explanation:
5\(\frac{3}{7}\) ÷ 2\(\frac{2}{3}\)
= \(\frac{35 + 5}{7}\) ÷ \(\frac{6 + 2}{3}\)
= \(\frac{40}{7}\) ÷ \(\frac{8}{3}\)
= \(\frac{40}{7}\) x \(\frac{3}{8}\)
= \(\frac{40 X 3}{7 X 8}\)
= \(\frac{15}{7}\)
Question 4.
5\(\frac{2}{9}\) ÷ 3\(\frac{2}{7}\)
Answer:
1\(\frac{122}{207}\),
Explanation:
5\(\frac{2}{9}\) ÷ 3\(\frac{2}{7}\)
= \(\frac{45 + 2}{9}\) ÷ \(\frac{21 + 2}{7}\)
= \(\frac{47}{9}\) ÷ \(\frac{23}{7}\)
= \(\frac{47}{9}\) x \(\frac{7}{23}\)
= \(\frac{47 X 7}{9 X 23}\)
= \(\frac{329}{207}\)
=1\(\frac{122}{207}\),
Question 5.
7\(\frac{2}{5}\) ÷ 3\(\frac{3}{5}\)
Answer:
2\(\frac{1}{8}\),
Explanation:
7\(\frac{2}{5}\) ÷ 3\(\frac{3}{5}\)
= \(\frac{35 + 2}{5}\) ÷ \(\frac{15 + 3}{5}\)
= \(\frac{37}{5}\) ÷ \(\frac{18}{5}\)
= \(\frac{37}{5}\) x \(\frac{5}{18}\)
= \(\frac{37 X 5}{5 X 18}\)
= \(\frac{37}{18}\)
= 2\(\frac{1}{8}\)
Question 6.
4\(\frac{1}{4}\) ÷ 2\(\frac{3}{7}\)
Answer:
1\(\frac{3}{4}\),
Explanation:
4\(\frac{1}{4}\) ÷ 2\(\frac{3}{7}\)
= \(\frac{35 + 2}{5}\) ÷ \(\frac{15 + 3}{5}\)
= \(\frac{37}{5}\) ÷ \(\frac{18}{5}\)
= \(\frac{37}{5}\) x \(\frac{5}{18}\)
= \(\frac{37 X 5}{5 X 18}\)
= \(\frac{37}{18}\)
= 2\(\frac{1}{18}\)
Question 7.
3\(\frac{4}{9}\) ÷ 3\(\frac{2}{9}\)
Answer:
1\(\frac{2}{29}\),
Explanation:
3\(\frac{4}{9}\) ÷ 3\(\frac{2}{9}\)
= \(\frac{27 + 4}{9}\) ÷ \(\frac{27 + 2}{9}\)
= \(\frac{31}{9}\) ÷ \(\frac{29}{9}\)
= \(\frac{31}{9}\) x \(\frac{9}{29}\)
= \(\frac{31 X 9}{9 X 29}\)
= \(\frac{31}{29}\)
= 1\(\frac{2}{29}\)
Question 8.
3\(\frac{4}{11}\) ÷ 5\(\frac{1}{2}\)
Answer:
\(\frac{74}{121}\),
Explanation:
3\(\frac{4}{11}\) ÷ 5\(\frac{1}{2}\)
= \(\frac{33 + 4}{11}\) ÷ \(\frac{10 + 1}{2}\)
= \(\frac{37}{11}\) ÷ \(\frac{11}{2}\)
= \(\frac{37}{11}\) x \(\frac{2}{11}\)
= \(\frac{37 X 2}{11 X 11}\)
= \(\frac{74}{121}\)
Question 9.
4\(\frac{7}{13}\) ÷ 2\(\frac{2}{3}\)
Answer:
1\(\frac{73}{104}\),
Explanation:
4\(\frac{7}{13}\) ÷ 2\(\frac{2}{3}\)
= \(\frac{52 + 7}{13}\) ÷ \(\frac{6 + 2}{3}\)
= \(\frac{59}{13}\) ÷ \(\frac{8}{3}\)
= \(\frac{59}{13}\) x \(\frac{3}{8}\)
= \(\frac{59 X 3}{13 X 8}\)
= \(\frac{177}{104}\)
= 1\(\frac{73}{104}\)
Question 10.
3\(\frac{7}{13}\) ÷ 1\(\frac{5}{8}\)
Answer:
2\(\frac{30}{169}\),
Explanation:
3\(\frac{7}{13}\) ÷ 1\(\frac{5}{8}\)
= \(\frac{39 + 7}{13}\) ÷ \(\frac{8 + 5}{8}\)
= \(\frac{46}{13}\) ÷ \(\frac{13}{8}\)
= \(\frac{46}{13}\) x \(\frac{8}{13}\)
= \(\frac{46 X 8}{13 X 13}\)
= \(\frac{368}{169}\)
= 2\(\frac{30}{169}\),
Question 11.
1\(\frac{6}{7}\) ÷ 2\(\frac{2}{9}\)
Answer:
\(\frac{117}{140}\),
Explanation:
1\(\frac{6}{7}\) ÷ 2\(\frac{2}{9}\)
= \(\frac{7 + 6}{7}\) ÷ \(\frac{18 + 2}{9}\)
= \(\frac{13}{7}\) ÷ \(\frac{20}{9}\)
= \(\frac{13}{7}\) x \(\frac{9}{20}\)
= \(\frac{13 X 9}{7 X 20}\)
= \(\frac{117}{140}\)
Question 12.
3\(\frac{5}{8}\) ÷ 1\(\frac{7}{8}\)
Answer:
1\(\frac{14}{15}\)
Explanation:
3\(\frac{5}{8}\) ÷ 1\(\frac{7}{8}\)
= \(\frac{24 + 5}{8}\) ÷ \(\frac{8 + 7}{8}\)
= \(\frac{29}{8}\) ÷ \(\frac{15}{8}\)
= \(\frac{29}{8}\) x \(\frac{8}{15}\)
= \(\frac{29 X 8}{8 X 15}\)
= \(\frac{29}{15}\)
= 1\(\frac{14}{15}\)
Question 13.
2\(\frac{4}{7}\) ÷ 4\(\frac{1}{3}\)
Answer:
\(\frac{54}{91}\)
Explanation:
2\(\frac{4}{7}\) ÷ 4\(\frac{1}{3}\)
= \(\frac{14 + 4}{7}\) ÷ \(\frac{12 + 1}{3}\)
= \(\frac{18}{7}\) ÷ \(\frac{13}{3}\)
= \(\frac{18}{7}\) x \(\frac{3}{13}\)
= \(\frac{18 X 3}{7 x 13}\)
= \(\frac{54}{91}\)
Question 14.
6\(\frac{1}{2}\) ÷ 2\(\frac{1}{2}\)
Answer:
2\(\frac{3}{5}\),
Explanation:
6\(\frac{1}{2}\) ÷ 2\(\frac{1}{2}\)
= \(\frac{12 + 1}{2}\) ÷ \(\frac{4 + 1}{2}\)
= \(\frac{13}{2}\) ÷ \(\frac{5}{2}\)
= \(\frac{13}{2}\) x \(\frac{2}{5}\)
= \(\frac{13 X 2}{2 x 5}\)
= \(\frac{13}{5}\)
= 2\(\frac{3}{5}\)
Question 15.
7\(\frac{3}{5}\) ÷ 1\(\frac{4}{5}\)
Answer:
4\(\frac{2}{9}\),
Explanation:
7\(\frac{3}{5}\) ÷ 1\(\frac{4}{5}\)
= \(\frac{35 + 3}{5}\) ÷ \(\frac{5 + 4}{5}\)
= \(\frac{38}{5}\) ÷ \(\frac{9}{5}\)
= \(\frac{38}{5}\) x \(\frac{5}{9}\)
= \(\frac{38 X 5}{5 x 9}\)
= \(\frac{38}{9}\)
= 4\(\frac{2}{9}\)
Question 16.
1\(\frac{2}{9}\) ÷ 3\(\frac{1}{7}\)
Answer:
\(\frac{7}{18}\)
Explanation:
1\(\frac{2}{9}\) ÷ 3\(\frac{1}{7}\)
= \(\frac{9 + 2}{9}\) ÷ \(\frac{21 + 1}{7}\)
= \(\frac{11}{9}\) ÷ \(\frac{22}{7}\)
= \(\frac{11}{9}\) x \(\frac{7}{22}\)
=\(\frac{11 X 7}{9 x 22}\)
=\(\frac{7}{18}\)
Question 17.
Ursula ran for 1\(\frac{3}{4}\) hours. If she ran 3\(\frac{3}{4}\) miles in total, how fast did she run in miles per hour?
Answer:
2\(\frac{1}{7}\) miles/hour,
Explanation:
Speed = Distance ÷ Time
Speed = 3\(\frac{3}{4}\) ÷1\(\frac{3}{4}\)
= \(\frac{12 + 3}{4}\) ÷ \(\frac{4 + 3}{4}\)
= \(\frac{15}{4}\) ÷ \(\frac{7}{4}\)
= \(\frac{15}{4}\) x \(\frac{4}{7}\)
= \(\frac{15 X 4}{4 x 7}\)
= \(\frac{15}{7}\)
= 2\(\frac{1}{7}\)
Question 18.
Mason sorted 14\(\frac{5}{8}\) pounds of laundry into 2\(\frac{1}{2}\) loads. How many pounds were in each load?
Answer:
5\(\frac{17}{20}\) pounds,
Explanation:
14\(\frac{5}{8}\) ÷ 2\(\frac{1}{2}\)
= \(\frac{112 + 5}{8}\) ÷ \(\frac{4 +1}{2}\)
= \(\frac{117}{8}\) ÷ \(\frac{5}{2}\)
= \(\frac{117}{8}\) x \(\frac{2}{5}\)
= \(\frac{117 X 2}{8 x 5}\)
=\(\frac{117}{20}\)
= 5\(\frac{17}{20}\)