McGraw Hill Math Grade 8 Lesson 5.4 Answer Key Dividing Mixed Numbers

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\(\frac{17}{20}\).