McGraw Hill Math Grade 8 Lesson 4.3 Answer Key Multiplying Fractions and Mixed Numbers

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 4.3 Multiplying Fractions and Mixed Numbers to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 4.3 Multiplying Fractions and Mixed Numbers

Exercises Multiply

Question 1.
6\(\frac{3}{4}\) × \(\frac{1}{9}\)
Answer:
\(\frac{3}{4}\),

Explanation:
We have 6\(\frac{3}{4}\) X \(\frac{1}{9}\),
Step 1:
Change the mixed number into improper fraction as
\(\frac{6 X 4  +  3}{4}\) = \(\frac{27}{4}\),
Step 2:
Multiplying the fractions as \(\frac{27}{4}\) X \(\frac{1}{9}\) = \(\frac{27 X 1}{4  X  9}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{27}{36}\) = \(\frac{9 X 3}{9 X 4}\) = \(\frac{3}{4}\).

Question 2.
\(\frac{1}{10}\) × 4\(\frac{1}{6}\)
Answer:
\(\frac{5}{12}\),

Explanation:
We have \(\frac{1}{10}\) X 4\(\frac{1}{6}\),
Step 1:
Change the mixed number into improper fraction as
\(\frac{4 X 6  +  1}{6}\) = \(\frac{25}{6}\),
Step 2:
Multiplying the fractions as \(\frac{1}{10}\) X \(\frac{25}{6}\) = \(\frac{1 X 25}{10 X  6}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{25}{60}\) = \(\frac{5 X 5}{5 X 2 X 6}\) = \(\frac{5}{12}\).

Question 3.
12\(\frac{1}{4}\) × \(\frac{2}{7}\)
Answer:
14,

Explanation:
We have 12\(\frac{1}{4}\) X \(\frac{2}{7}\),
Step 1:
Change the mixed number into improper fraction as
\(\frac{12 X 4  +  1}{4}\) = \(\frac{49}{4}\),
Step 2:
Multiplying the fractions as \(\frac{49}{4}\) X \(\frac{2}{7}\) = \(\frac{49 X 4}{2 X 7}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{7 X 7 X 2 X 2}{2 X 7}\) = 7 X 2 = 14.

Question 4.
3\(\frac{1}{7}\) × \(\frac{14}{11}\)
Answer:
4,

Explanation:
We have 3\(\frac{1}{7}\) X \(\frac{14}{11}\),
Step 1:
Change the mixed number into improper fraction as
\(\frac{3 X 7  +  1}{7}\) = \(\frac{22}{7}\),
Step 2:
Multiplying the fractions as \(\frac{22}{7}\) X \(\frac{14}{11}\) = \(\frac{22 X 14}{7 X  11}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{308}{77}\) = \(\frac{4 X 11 X 7}{7 X 11}\) = 4.

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

Explanation:
We have \(\frac{2}{5}\) X 3\(\frac{3}{4}\)
Step 1:
Change the mixed number into improper fraction as
\(\frac{3 X 4  +  3}{4}\) = \(\frac{15}{4}\),
Step 2:
Multiplying the fractions as \(\frac{2}{5}\) X \(\frac{15}{4}\) = \(\frac{2 X 15}{ X  11}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{308}{77}\) = \(\frac{4 X 11 X 7}{7 X 11}\) = 4.

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

Explanation:
We have 4\(\frac{5}{7}\) X \(\frac{7}{11}\)
Step 1:
Change the mixed number into improper fraction as
\(\frac{4 X 7  +  5}{7}\) = \(\frac{33}{7}\),
Step 2:
Multiplying the fractions as \(\frac{33}{7}\) X \(\frac{7}{11}\) = \(\frac{221}{77}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{221}{77}\) = \(\frac{3 X 11 X 7}{7 X 11}\) = 3.

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

Explanation:
We have 4\(\frac{2}{5}\) X \(\frac{3}{11}\)
Step 1:
Change the mixed number into improper fraction as
\(\frac{4 X 5  + 2}{5}\) = \(\frac{22}{5}\),
Step 2:
Multiplying the fractions as \(\frac{22}{5}\) X \(\frac{3}{11}\) = \(\frac{66}{55}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{66}{55}\) = \(\frac{6 X 11}{5 X 11}\) = \(\frac{6}{5}\)
as numerator is greater than denominator \(\frac{1 X 5 + 1}{5}\) = 1\(\frac{1}{5}\).

Question 8.
3\(\frac{1}{4}\) × \(\frac{4}{13}\)
Answer:
1,

Explanation:
We have 3\(\frac{1}{4}\) X \(\frac{4}{13}\)
Step 1:
Change the mixed number into improper fraction as
\(\frac{3 X 4  +  1}{4}\) = \(\frac{13}{4}\),
Step 2:
Multiplying the fractions as \(\frac{13}{4}\) X \(\frac{4}{13}\) = 3.

Question 9.
3\(\frac{3}{5}\) × \(\frac{10}{9}\)
Answer:
4,

Explanation:
We have 3\(\frac{3}{5}\) X \(\frac{10}{9}\)
Step 1:
Change the mixed number into improper fraction as
\(\frac{3 X 5  +  3}{5}\) = \(\frac{18}{5}\),
Step 2:
Multiplying the fractions as \(\frac{18}{5}\) X \(\frac{10}{9}\) = \(\frac{180}{45}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{180}{45}\) = \(\frac{45 X 4}{45}\) = 4.

Question 10.
\(\frac{3}{13}\) × 4\(\frac{1}{3}\)
Answer:
1,

Explanation:
We have \(\frac{3}{13}\) X 4\(\frac{1}{3}\)
Step 1:
Change the mixed number into improper fraction as
\(\frac{4 X 3  +  1}{3}\) = \(\frac{13}{3}\),
Step 2:
Multiplying the fractions as \(\frac{3}{13}\) X \(\frac{13}{3}\) = 1.

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

Explanation:
We have 3\(\frac{2}{3}\) X \(\frac{2}{11}\)
Step 1:
Change the mixed number into improper fraction as
\(\frac{3 X 3  +  2}{3}\) = \(\frac{11}{3}\),
Step 2:
Multiplying the fractions as \(\frac{11}{3}\) X \(\frac{2}{11}\) = \(\frac{22}{33}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{22}{33}\) = \(\frac{2 X 11}{3 X 11}\) = \(\frac{2}{3}\).

Question 12.
5\(\frac{1}{5}\) × \(\frac{3}{13}\)
Answer:
\(\frac{6}{5}\),

Explanation:
We have 5\(\frac{1}{5}\) X \(\frac{3}{13}\)
Step 1:
Change the mixed number into improper fraction as
\(\frac{5 X 5 + 1}{5}\) = \(\frac{26}{5}\),
Step 2:
Multiplying the fractions as \(\frac{26}{5}\) X \(\frac{3}{13}\) = \(\frac{78}{65}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{78}{65}\) = \(\frac{6 X 13}{5 X 13}\) =\(\frac{6}{5}\).

Question 13.
5\(\frac{1}{4}\) × \(\frac{1}{3}\)
Answer:
\(\frac{7}{4}\),

Explanation:
We have 5\(\frac{1}{4}\) X \(\frac{1}{3}\)
Step 1:
Change the mixed number into improper fraction as
\(\frac{5 X 4  +  1}{4}\) = \(\frac{21}{4}\),
Step 2:
Multiplying the fractions as \(\frac{26}{5}\) X \(\frac{3}{13}\) = \(\frac{78}{65}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{78}{65}\) = \(\frac{6 X 13}{5 X 13}\) =\(\frac{6}{5}\).

Question 14.
2\(\frac{4}{5}\) × \(\frac{2}{7}\)
Answer:
\(\frac{4}{5}\),

Explanation:
We have 2\(\frac{4}{5}\) X \(\frac{2}{7}\)
Step 1:
Change the mixed number into improper fraction as
\(\frac{2 X 5  + 4}{5}\) = \(\frac{14}{5}\),
Step 2:
Multiplying the fractions as \(\frac{14}{5}\) X \(\frac{2}{7}\) = \(\frac{28}{35}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{28}{35}\) = \(\frac{7 X 4}{7 X 5}\) =\(\frac{4}{5}\).

Question 15.
2\(\frac{1}{4}\) × \(\frac{3}{10}\)
Answer:
\(\frac{27}{40}\),

Explanation:
We have 2\(\frac{1}{4}\) X \(\frac{3}{10}\)
Step 1:
Change the mixed number into improper fraction as
\(\frac{2 X 4  +  1}{4}\) = \(\frac{9}{4}\),
Step 2:
Multiplying the fractions as \(\frac{9}{4}\) X \(\frac{3}{10}\) = \(\frac{27}{40}\) as numerator is smaller we cannot reduce further.

Question 16.
3\(\frac{1}{3}\) × \(\frac{3}{5}\)
Answer:
2,

Explanation:
We have 3\(\frac{1}{3}\) X \(\frac{3}{5}\)
Step 1:
Change the mixed number into improper fraction as
\(\frac{3 X 3 + 1}{3}\) = \(\frac{10}{3}\),
Step 2:
Multiplying the fractions as \(\frac{10}{3}\) X \(\frac{3}{5}\) = 2.

Question 17.
Thomas can walk on his hands 20\(\frac{2}{5}\) yards in a minute. How far can he go in \(\frac{3}{4}\) minutes?
Answer:
Thomas can walk 15\(\frac{3}{10}\) minutes,

Explanation:
As Thomas can walk on his hands 20\(\frac{2}{5}\) yards in a minute.
Far can he go in \(\frac{3}{4}\) minutes is 20\(\frac{2}{5}\) X \(\frac{3}{5}\)
Step 1:
Change the mixed number into improper fraction as
\(\frac{20 X 5  + 2}{5}\) = \(\frac{102}{15}\),
Step 2:
Multiplying the fractions as \(\frac{102}{15}\) X \(\frac{3}{5}\) = \(\frac{306}{75}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{306}{75}\) = \(\frac{153}{10}\) = 15\(\frac{3}{10}\).
Therefore, Thomas can walk 15\(\frac{3}{10}\) minutes,

Question 18.
Peyton plays a round of golf in 3\(\frac{3}{8}\) hours. How long would it take him to play \(\frac{2}{3}\) rounds of golf?
Answer:
Peyton took 2\(\frac{1}{4}\) rounds of golf’s,

Explanation:
Given Peyton plays a round of golf in 3\(\frac{3}{8}\) hours. Long would it take him to play \(\frac{2}{3}\) rounds of golf is 3\(\frac{3}{8}\) X \(\frac{2}{3}\), So \(\frac{3 X 8 + 3}{8}\) X \(\frac{2}{3}\) = \(\frac{27}{8}\) X \(\frac{2}{3}\) = \(\frac{27 X 2}{8 X 3}\) = \(\frac{54}{24}\) both goes by 6 we get \(\frac{6 X 9}{6 X 4}\) = \(\frac{9}{4}\) =
as numerator is more than denominator \(\frac{2 X 4 + 1}{4}\) = 2\(\frac{1}{4}\). Peyton took 2\(\frac{1}{4}\) rounds of golf’s.