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McGraw-Hill Math Grade 7 Answer Key Lesson 7.3 Multiplying Mixed Numbers: Reducing
Exercises Multiply
Question 1.
5\(\frac{1}{4}\) × \(\frac{1}{2}\)
Answer:
2\(\frac{5}{8}\)
Explanation:
5\(\frac{1}{4}\) × \(\frac{1}{2}\)
Convert mixed fraction into simplest fraction.
= \(\frac{21}{4}\) × \(\frac{1}{2}\)
Multiply the numerators to get the numerator of the product,
then multiply the denominators to get the denominators of the product.
= \(\frac{21 X 1}{4 X 2}\)
= \(\frac{21}{8}\)
= 5\(\frac{5}{8}\)
Question 2.
\(\frac{1}{3}\) × 5\(\frac{1}{3}\)
Answer:
1\(\frac{7}{9}\)
Explanation:
\(\frac{1}{3}\) × 5\(\frac{1}{3}\)
Convert mixed fraction into simplest fraction.
= \(\frac{1}{3}\) × \(\frac{16}{3}\)
Multiply the numerators to get the numerator of the product,
then multiply the denominators to get the denominators of the product.
= \(\frac{1 X 16}{3 X 3}\)
= \(\frac{16}{9}\)
= 1\(\frac{7}{9}\)
Question 3.
-12\(\frac{1}{4}\) × \(\frac{3}{2}\)
Answer:
-18\(\frac{3}{8}\)
Explanation:
-12\(\frac{1}{4}\) × \(\frac{3}{2}\)
Convert mixed fraction into simplest fraction.
= –\(\frac{49}{4}\) × \(\frac{3}{2}\)
Multiply the numerators to get the numerator of the product,
then multiply the denominators to get the denominators of the product.
= –\(\frac{49 X 3}{4 X 2}\)
= –\(\frac{147}{8}\)
= -12\(\frac{3}{8}\)
Question 4.
3\(\frac{1}{7}\) × \(\frac{14}{3}\)
Answer:
14\(\frac{2}{3}\)
Explanation:
3\(\frac{1}{7}\) × \(\frac{14}{3}\)
Convert mixed fraction into simplest fraction.
= \(\frac{22}{7}\) × \(\frac{14}{3}\)
Multiply the numerators to get the numerator of the product,
then multiply the denominators to get the denominators of the product.
= \(\frac{22 X 14}{7 X 3}\)
= \(\frac{308}{21}\)
= \(\frac{44}{3}\)
= 14\(\frac{2}{3}\)
Question 5.
–\(\frac{1}{5}\) × 1\(\frac{3}{4}\)
Answer:
–\(\frac{7}{20}\)
Explanation:
–\(\frac{1}{5}\) × 1\(\frac{3}{4}\)
Convert mixed fraction into simplest fraction.
= –\(\frac{1}{5}\) × \(\frac{7}{4}\)
Multiply the numerators to get the numerator of the product,
then multiply the denominators to get the denominators of the product.
= –\(\frac{1 X 7}{5 X 4}\)
= –\(\frac{7}{20}\)
Question 6.
6\(\frac{5}{7}\) × \(\frac{2}{3}\)
Answer:
4\(\frac{10}{21}\)
Explanation:
6\(\frac{5}{7}\) × \(\frac{2}{3}\)
Convert mixed fraction into simplest fraction.
= \(\frac{47}{7}\) × \(\frac{2}{3}\)
Multiply the numerators to get the numerator of the product,
then multiply the denominators to get the denominators of the product.
= \(\frac{47 X 2}{7 X 3}\)
= \(\frac{94}{21}\)
= 4\(\frac{10}{21}\)
Question 7.
4\(\frac{2}{5}\) × \(\frac{3}{8}\)
Answer:
1\(\frac{13}{20}\)
Explanation:
4\(\frac{2}{5}\) × \(\frac{3}{8}\)
Convert mixed fraction into simplest fraction.
= \(\frac{22}{5}\) × \(\frac{3}{8}\)
Multiply the numerators to get the numerator of the product,
then multiply the denominators to get the denominators of the product.
= \(\frac{22 X 3}{5 X 8}\)
= \(\frac{66}{40}\)
= \(\frac{33}{20}\)
= 1\(\frac{13}{20}\)
Question 8.
3\(\frac{1}{4}\) × \(\frac{5}{8}\)
Answer:
2\(\frac{1}{32}\)
Explanation:
3\(\frac{1}{4}\) × \(\frac{5}{8}\)
Convert mixed fraction into simplest fraction.
= \(\frac{13}{4}\) × \(\frac{5}{8}\)
Multiply the numerators to get the numerator of the product,
then multiply the denominators to get the denominators of the product.
= \(\frac{13 X 5}{4 X 8}\)
= \(\frac{65}{32}\)
= 2\(\frac{1}{32}\)
Question 9.
3\(\frac{2}{5}\) × \(\frac{5}{9}\)
Answer:
1\(\frac{8}{9}\)
Explanation:
3\(\frac{2}{5}\) × \(\frac{5}{9}\)
Convert mixed fraction into simplest fraction.
= \(\frac{17}{5}\) × \(\frac{5}{9}\)
Multiply the numerators to get the numerator of the product,
then multiply the denominators to get the denominators of the product.
= \(\frac{17 X 5}{5 X 9}\)
= \(\frac{85}{45}\)
= \(\frac{17}{9}\)
= 1\(\frac{8}{9}\)
Question 10.
\(\frac{1}{4}\) × 4\(\frac{1}{3}\)
Answer:
1\(\frac{1}{12}\)
Explanation:
\(\frac{1}{4}\) × 4\(\frac{1}{3}\)
Convert mixed fraction into simplest fraction.
= \(\frac{1}{4}\) × \(\frac{13}{3}\)
Multiply the numerators to get the numerator of the product,
then multiply the denominators to get the denominators of the product.
= \(\frac{1 X 13}{4 X 3}\)
= \(\frac{13}{12}\)
= 1\(\frac{1}{12}\)
Question 11.
3\(\frac{2}{3}\) × 1\(\frac{2}{7}\)
Answer:
4\(\frac{5}{7}\)
Explanation:
3\(\frac{2}{3}\) × 1\(\frac{2}{7}\)
Convert mixed fraction into simplest fraction.
= \(\frac{11}{3}\) × \(\frac{9}{7}\)
Multiply the numerators to get the numerator of the product,
then multiply the denominators to get the denominators of the product.
= \(\frac{11 X 9}{3 X 7}\)
= \(\frac{99}{21}\)
= \(\frac{33}{7}\)
= 4\(\frac{5}{7}\)
Question 12.
-4\(\frac{1}{5}\) × -2\(\frac{3}{14}\)
Answer:
9\(\frac{3}{10}\)
Explanation:
-4\(\frac{1}{5}\) × -2\(\frac{3}{14}\)
Convert mixed fraction into simplest fraction.
= –\(\frac{21}{5}\) × –\(\frac{31}{14}\)
Multiply the numerators to get the numerator of the product,
then multiply the denominators to get the denominators of the product.
= \(\frac{21 X 31}{5 X 14}\)
= \(\frac{651}{70}\)
= \(\frac{93}{10}\)
= 9\(\frac{3}{10}\)
Question 13.
5\(\frac{1}{4}\) × 3\(\frac{1}{3}\)
Answer:
17\(\frac{1}{2}\)
Explanation:
5\(\frac{1}{4}\) × 3\(\frac{1}{3}\)
Convert mixed fraction into simplest fraction.
= \(\frac{21}{4}\) × \(\frac{10}{3}\)
Multiply the numerators to get the numerator of the product,
then multiply the denominators to get the denominators of the product.
= \(\frac{21 X 10}{4 X 3}\)
= \(\frac{210}{12}\)
= \(\frac{35}{2}\)
= 17\(\frac{1}{2}\)
Question 14.
-2\(\frac{4}{5}\) × -4\(\frac{2}{7}\)
Answer:
12
Explanation:
-2\(\frac{4}{5}\) × -4\(\frac{2}{7}\)
Convert mixed fraction into simplest fraction.
= –\(\frac{14}{5}\) × –\(\frac{30}{7}\)
Multiply the numerators to get the numerator of the product,
then multiply the denominators to get the denominators of the product.
= \(\frac{14 X 30}{5 X 7}\)
= \(\frac{520}{35}\)
= 12
Question 15.
3\(\frac{3}{4}\) × 3\(\frac{3}{10}\)
Answer:
12\(\frac{3}{8}\)
Explanation:
3\(\frac{3}{4}\) × 3\(\frac{3}{10}\)
Convert mixed fraction into simplest fraction.
= \(\frac{15}{4}\) × \(\frac{33}{10}\)
Multiply the numerators to get the numerator of the product,
then multiply the denominators to get the denominators of the product.
= \(\frac{15 X 33}{4 X 10}\)
= \(\frac{495}{40}\)
= \(\frac{99}{8}\)
= 12\(\frac{3}{8}\)
Question 16.
3\(\frac{1}{3}\) × 3\(\frac{3}{5}\)
Answer:
12
Explanation:
3\(\frac{1}{3}\) × 3\(\frac{3}{5}\)
Convert mixed fraction into simplest fraction.
= \(\frac{10}{3}\) × \(\frac{18}{5}\)
Multiply the numerators to get the numerator of the product,
then multiply the denominators to get the denominators of the product.
= \(\frac{10 X 18}{3 X 5}\)
= \(\frac{180}{15}\)
= 12