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Exercises Numbers, fractions and percents

Example 4.29 from Prealgebra, 4.2 Multiply and Divide Fractions

Multiply and Divide Fractions: example 4.29

Find the reciprocal of each number. Then check that the product of each number and its reciprocal is $1 .$

ⓐ $\frac{4}{9}$
ⓑ $- \frac{1}{6}$
ⓒ $- \frac{14}{5}$
ⓓ $7$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
To find the reciprocals, we keep the sign and invert the fractions.

ⓐ

Find the reciprocal of $\frac{4}{9}$ . The reciprocal of $\frac{4}{9}$ is $\frac{9}{4}$ .

Check:

Multiply the number and its reciprocal. $\frac{4}{9} \cdot \frac{9}{4}$

Multiply numerators and denominators. $\frac{36}{36}$

Simplify. $1 ✓$

ⓑ

Find the reciprocal of $- \frac{1}{6}$ . $- \frac{6}{1}$

Simplify. $- 6$

Check: $- \frac{1}{6} \cdot (- 6)$

$1 ✓$

ⓒ

Find the reciprocal of $- \frac{14}{5}$ . $- \frac{5}{14}$

Check: $- \frac{14}{5} \cdot (- \frac{5}{14})$

$\frac{70}{70}$

$1 ✓$

ⓓ

Find the reciprocal of $\frac{5}{7}$ .

Write $7$ as a fraction. $\frac{7}{1}$

Write the reciprocal of $\frac{7}{1}$ . $\frac{1}{7}$

Check: $7 \cdot (\frac{1}{7})$

$1 ✓$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Find the reciprocal:

ⓐ $\frac{5}{7}$
ⓑ $- \frac{1}{8}$
ⓒ $- \frac{11}{4}$
ⓓ $14$

How did it go?

PreviousMultiply and Divide Fractions: example 4.28 Next Multiply and Divide Fractions: example 4.30

From Prealgebra (1st edition) by OpenStax (Rice University), section 4.2, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.