McGraw Hill Math Grade 8 Lesson 4.4 Answer Key Multiplying Mixed Numbers

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 4.4 Multiplying Mixed Numbers to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 4.4 Multiplying Mixed Numbers

Exercises Multiply

Question 1.
5\(\frac{1}{2}\) × 3\(\frac{3}{4}\)
Answer:
20\(\frac{5}{8}\),

Explanation:
We have 5\(\frac{1}{2}\) X 3\(\frac{3}{4}\),
Step 1:
Change the mixed number into improper fraction as
\(\frac{5 X 2  +  1}{2}\) = \(\frac{11}{2}\) and
3\(\frac{3}{4}\) = \(\frac{3 X 4 + 3}{4}\) = \(\frac{15}{4}\),
Step 2:
Multiplying the fractions as \(\frac{11}{2}\) X \(\frac{15}{4}\) = \(\frac{11 X 15}{2 X 4}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{165}{8}\) = \(\frac{20 X 8 + 5}{8}\) = 20\(\frac{5}{8}\).

Question 2.
2\(\frac{1}{3}\) × 2\(\frac{4}{5}\)
Answer:
6\(\frac{8}{15}\),

Explanation:
We have 2\(\frac{1}{3}\) X 2\(\frac{4}{5}\),
Step 1:
Change the mixed number into improper fraction as
\(\frac{6 X 3  +  1}{3}\) = \(\frac{2 X 5 + 4}{5}\),
Step 2:
Multiplying the fractions as \(\frac{7}{3}\) X \(\frac{14}{5}\) =
\(\frac{7 X 14}{3  X  5}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{98}{15}\) = \(\frac{15 X 6 + 8}{15}\) = 6\(\frac{8}{15}\).

Question 3.
8\(\frac{1}{5}\) × 3\(\frac{1}{7}\)
Answer:
25\(\frac{27}{35}\),

Explanation:
We have 8\(\frac{1}{5}\) X 3\(\frac{1}{7}\)
Step 1:
Change the mixed number into improper fraction as
\(\frac{8 X 5  +  1}{5}\) = \(\frac{41}{5}\) and
3\(\frac{1}{7}\) = \(\frac{3 X 7 + 1}{7}\) = \(\frac{22}{7}\),
Step 2:
Multiplying the fractions as \(\frac{41}{5}\) X \(\frac{22}{7}\) =
\(\frac{41 X 22}{5  X  7}\) = \(\frac{902}{35}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{902}{35}\) = \(\frac{25 X 35 + 27}{35}\) = 25\(\frac{27}{35}\).

Question 4.
1\(\frac{3}{4}\) × 12\(\frac{1}{3}\)
Answer:
21\(\frac{7}{12}\),

Explanation:
We have 1\(\frac{3}{4}\) X 12\(\frac{1}{3}\)
Step 1:
Change the mixed number into improper fraction as
\(\frac{1 X 4 + 3}{4}\) = \(\frac{7}{4}\) and
12\(\frac{1}{3}\) = \(\frac{12 X 3 + 1}{3}\) = \(\frac{37}{3}\),
Step 2:
Multiplying the fractions as \(\frac{7}{4}\) X \(\frac{37}{3}\) =
\(\frac{7 X 37}{4  X  3}\) = \(\frac{259}{12}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{259}{12}\) = \(\frac{21 X 12 + 7}{12}\) = 21\(\frac{7}{12}\).

Question 5.
2\(\frac{1}{2}\) × 4\(\frac{2}{3}\)
Answer:
11\(\frac{2}{3}\),

Explanation:
We have 2\(\frac{1}{2}\) X 4\(\frac{2}{3}\)
Step 1:
Change the mixed number into improper fraction as
\(\frac{2 X 2 + 1}{2}\) = \(\frac{5}{2}\) and
4\(\frac{2}{3}\) = \(\frac{4 X 3 + 2}{3}\) = \(\frac{14}{3}\),
Step 2:
Multiplying the fractions as \(\frac{5}{2}\) X \(\frac{14}{3}\) =
\(\frac{5 X 14}{2 X 3}\) = \(\frac{70}{6}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{70}{6}\) = \(\frac{35}{3}\) = 11\(\frac{2}{3}\).

Question 6.
3\(\frac{1}{8}\) × 3\(\frac{1}{7}\)
Answer:
9\(\frac{23}{28}\),

Explanation:
We have 3\(\frac{1}{8}\) X 3\(\frac{1}{7}\)
Step 1:
Change the mixed number into improper fraction as
\(\frac{3 X 8 + 1}{8}\) = \(\frac{25}{8}\) and
3\(\frac{1}{7}\) = \(\frac{3 X 7 + 1}{7}\) = \(\frac{22}{7}\),
Step 2:
Multiplying the fractions as \(\frac{25}{2}\) X \(\frac{22}{7}\) =
\(\frac{25 X 22}{8 X 7}\) = \(\frac{550}{56}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{550}{56}\) = \(\frac{275}{28}\) =
9\(\frac{23}{28}\).

Question 7.
11\(\frac{1}{5}\) × 6\(\frac{2}{3}\)
Answer:
74\(\frac{2}{3}\),

Explanation:
We have 11\(\frac{1}{5}\) X 6\(\frac{2}{3}\)
Step 1:
Change the mixed number into improper fraction as
\(\frac{11 X 5 + 1}{5}\) = \(\frac{56}{5}\) and
6\(\frac{2}{3}\) = \(\frac{6 X 3 + 2}{3}\) = \(\frac{20}{3}\),
Step 2:
Multiplying the fractions as \(\frac{56}{5}\) X \(\frac{20}{3}\) =
\(\frac{56 X 20}{5 X 3}\) = \(\frac{1,120}{15}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{1,120}{15}\) = \(\frac{56 X 5 X 4}{5 X 3}\) = \(\frac{224}{3}\) = 74\(\frac{2}{3}\).

Question 8.
9\(\frac{1}{2}\) × 5\(\frac{1}{5}\)
Answer:
49\(\frac{2}{5}\),

Explanation:
We have 9\(\frac{1}{2}\) X 5\(\frac{1}{5}\)
Step 1:
Change the mixed number into improper fraction as
\(\frac{9 X 2 + 1}{2}\) = \(\frac{19}{2}\) and
5\(\frac{1}{5}\) = \(\frac{5 X 5 + 1}{5}\) = \(\frac{26}{5}\),
Step 2:
Multiplying the fractions as \(\frac{19}{2}\) X \(\frac{26}{5}\) =
\(\frac{19 X 26}{2 X 5}\) = \(\frac{494}{10}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{494}{10}\) = \(\frac{247 X 2}{5 X 2}\) = \(\frac{247}{5}\) = 49\(\frac{2}{5}\).

Question 9.
1\(\frac{2}{3}\) × 7\(\frac{1}{5}\)
Answer:
12,

Explanation:
We have 1\(\frac{2}{3}\) X 7\(\frac{1}{5}\)
Step 1:
Change the mixed number into improper fraction as
\(\frac{1 X 3 + 2}{3}\) = \(\frac{5}{3}\) and
7\(\frac{1}{5}\) = \(\frac{7 X 5 + 1}{5}\) = \(\frac{36}{5}\),
Step 2:
Multiplying the fractions as \(\frac{5}{3}\) X \(\frac{36}{5}\) =
\(\frac{5 X 36}{3 X 5}\) = \(\frac{180}{15}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{180}{15}\) = \(\frac{15 X 12 }{15}\)= 12.

Question 10.
8\(\frac{3}{4}\) × 3\(\frac{1}{2}\)
Answer:
23\(\frac{5}{8}\),

Explanation:
We have 8\(\frac{3}{4}\) X 3\(\frac{1}{2}\)
Step 1:
Change the mixed number into improper fraction as
\(\frac{8 X 4 + 3}{4}\) = \(\frac{27}{4}\) and
3\(\frac{1}{2}\) = \(\frac{3 X 2 + 1}{2}\) = \(\frac{7}{2}\),
Step 2:
Multiplying the fractions as \(\frac{27}{4}\) X \(\frac{7}{2}\) =
\(\frac{27 X 7}{4 X 2}\) = \(\frac{189}{8}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{189}{8}\) = \(\frac{23 X 8 + 5}{8}\) = 23\(\frac{5}{8}\).

Question 11.
3\(\frac{5}{8}\) × 5\(\frac{1}{4}\)
Answer:
19\(\frac{1}{32}\),

Explanation:
We have 3\(\frac{5}{8}\) X 5\(\frac{1}{4}\),
Step 1:
Change the mixed number into improper fraction as
\(\frac{3 X 8 + 5}{8}\) = \(\frac{29}{8}\) and
5\(\frac{1}{4}\) = \(\frac{5 X 4 + 1}{4}\) = \(\frac{21}{4}\),
Step 2:
Multiplying the fractions as \(\frac{29}{8}\) X \(\frac{21}{4}\) = \(\frac{29 X 21}{8 X 4}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{609}{32}\) = \(\frac{19 X 32 + 1}{32}\) = 19\(\frac{1}{32}\).

Question 12.
4\(\frac{2}{3}\) × 4\(\frac{1}{2}\)
Answer:
21,

Explanation:
We have 4\(\frac{2}{3}\) X 4\(\frac{1}{2}\),
Step 1:
Change the mixed number into improper fraction as
\(\frac{4 X 3 + 2}{3}\) = \(\frac{14}{3}\) and
4\(\frac{1}{2}\) = \(\frac{4 X 2 + 1}{2}\) = \(\frac{9}{2}\),
Step 2:
Multiplying the fractions as \(\frac{14}{3}\) X \(\frac{9}{2}\) = \(\frac{14 X 9}{3 X 2}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{126}{6}\) = 21.

Question 13.
3\(\frac{1}{5}\) × 2\(\frac{1}{10}\)
Answer:
6\(\frac{18}{25}\),

Explanation:
We have 3\(\frac{1}{5}\) X 2\(\frac{1}{10}\),
Step 1:
Change the mixed number into improper fraction as
\(\frac{3 X 5 + 1}{5}\) = \(\frac{16}{5}\) and
2\(\frac{1}{10}\) = \(\frac{2 X 10 + 1}{10}\) = \(\frac{21}{10}\),
Step 2:
Multiplying the fractions as \(\frac{16}{5}\) X \(\frac{21}{10}\) = \(\frac{16 X 21}{5 X 10}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{336}{50}\) = \(\frac{2 X 168}{2 X 25}\) = \(\frac{168}{25}\) = 6\(\frac{18}{25}\).

Question 14.
10\(\frac{4}{5}\) × 2\(\frac{1}{11}\)
Answer:
22\(\frac{32}{55}\),

Explanation:
We have 10\(\frac{4}{5}\) X 2\(\frac{1}{11}\),
Step 1:
Change the mixed number into improper fraction as
\(\frac{10 X 5 + 4}{5}\) = \(\frac{54}{5}\) and
2\(\frac{1}{11}\) = \(\frac{2 X 11 + 1}{11}\) = \(\frac{23}{11}\),
Step 2:
Multiplying the fractions as \(\frac{54}{5}\) X \(\frac{23}{11}\) = \(\frac{1,242}{55}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{1,242}{55}\) = \(\frac{22 X 55 + 32}{55}\) = 22\(\frac{32}{55}\).

Question 15.
22\(\frac{5}{9}\) × 1\(\frac{3}{5}\)
Answer:
36\(\frac{4}{45}\),

Explanation:
We have 22\(\frac{5}{9}\) X 1\(\frac{3}{5}\),
Step 1:
Change the mixed number into improper fraction as
\(\frac{22 X 9 + 5}{9}\) = \(\frac{203}{9}\) and
1\(\frac{3}{5}\) = \(\frac{1 X 5 + 3}{5}\) = \(\frac{8}{5}\),
Step 2:
Multiplying the fractions as \(\frac{203}{9}\) X \(\frac{8}{5}\) = \(\frac{203 X 8}{9 X 5}\) = \(\frac{1,624}{45}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{1,624}{45}\) = \(\frac{1,624}{45}\) = \(\frac{36 X 45 + 4}{45}\) = 36\(\frac{4}{45}\).

Question 16.
14\(\frac{3}{4}\) × 2\(\frac{5}{7}\)
Answer:
40\(\frac{1}{28}\),

Explanation:
We have 14\(\frac{3}{4}\) X 2\(\frac{5}{7}\),
Step 1:
Change the mixed number into improper fraction as
\(\frac{14 X 4 + 3}{4}\) = \(\frac{59}{4}\) and
2\(\frac{5}{7}\) = \(\frac{2 X 7 + 5}{7}\) = \(\frac{19}{7}\),
Step 2:
Multiplying the fractions as \(\frac{59}{4}\) X \(\frac{19}{7}\) = \(\frac{59 X 19}{4 X 7}\) = \(\frac{1,121}{28}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{1,121}{28}\) = \(\frac{40 X 28 + 1}{28}\) = 40\(\frac{1}{28}\).