Chapter 3

Add and subtract the following mixed numbers as indicated. \(1 \frac{5}{8}+2 \frac{1}{2}\)

Write your answers as proper fractions or mixed numbers, not as improper fractions. Find the following products. (Multiply.) $$\frac{2}{3} \cdot 4 \frac{9}{10}$$

Find each of the following products. (Multiply.) $$\frac{2}{9}\left(\frac{9}{2}\right)$$

Find the quotient in each case by replacing the divisor by its reciprocal and multiplying. $$\frac{4}{3} \div \frac{4}{3}$$

Find the following sums and differences, and reduce to lowest terms. (Add or subtract as indicated.) $$\frac{x+5}{4}-\frac{3}{4}$$

Factor each of the following into a product of prime factors. $$210$$

Use the rule for order of operations to simplify each of the following. [Examples 1–3] $$\left(1+\frac{5}{6}\right)\left(1-\frac{5}{6}\right)$$

Change each improper fraction to a mixed number. $$\frac{9}{8}$$

Add and subtract the following mixed numbers as indicated. \(7 \frac{5}{12}-3 \frac{1}{3}\)

Write your answers as proper fractions or mixed numbers, not as improper fractions. Find the following products. (Multiply.) $$2 \frac{1}{2} \cdot 3 \frac{1}{3} \cdot 1 \frac{1}{2}$$

Find each of the following products. (Multiply.) $$\frac{1}{2} \cdot \frac{1}{3} \cdot \frac{1}{4}$$

Find the quotient in each case by replacing the divisor by its reciprocal and multiplying. $$\frac{7}{8} \div \frac{8}{7}$$

Find the following sums and differences, and reduce to lowest terms. (Add or subtract as indicated.) $$\frac{1}{10}-\frac{3}{10}-\frac{4}{10}$$

Factor each of the following into a product of prime factors. $$215$$

Name the denominator of each fraction. $$\frac{a}{12}$$

Use the rule for order of operations to simplify each of the following. [Examples 1–3] $$\left(2-\frac{1}{4}\right)\left(2+\frac{1}{4}\right)$$

Change each improper fraction to a mixed number. $$\frac{10}{9}$$

Add and subtract the following mixed numbers as indicated. \(7 \frac{3}{4}-3 \frac{5}{12}\)

Write your answers as proper fractions or mixed numbers, not as improper fractions. Find the following products. (Multiply.) $$3 \frac{1}{5} \cdot 5 \frac{1}{6} \cdot 1 \frac{1}{8}$$

Find each of the following products. (Multiply.) $$\frac{2}{3} \cdot \frac{4}{5} \cdot \frac{1}{3}$$

Find the quotient in each case by replacing the divisor by its reciprocal and multiplying. $$\frac{4}{3} \div \frac{3}{4}$$

Find the following sums and differences, and reduce to lowest terms. (Add or subtract as indicated.) $$\frac{3}{20}-\frac{1}{20}-\frac{4}{20}$$

Factor each of the following into a product of prime factors. $$75$$

Name the denominator of each fraction. $$\frac{b}{14}$$

Use the rule for order of operations to simplify each of the following. [Examples 1–3] $$\frac{2}{3}+\frac{1}{3}\left(2 \frac{1}{2}+\frac{1}{2}\right)^{2}$$

Find each of the following products. (Multiply.) $$\frac{2}{5} \cdot \frac{3}{5} \cdot \frac{4}{5}$$

Change each improper fraction to a mixed number. $$\frac{19}{4}$$

Add and subtract the following mixed numbers as indicated. \(6 \frac{1}{3}-4 \frac{1}{4}\)

Write your answers as proper fractions or mixed numbers, not as improper fractions. Find the following products. (Multiply.) $$\frac{3}{4} \cdot 7 \cdot 1 \frac{4}{5}$$

Find the quotient in each case by replacing the divisor by its reciprocal and multiplying. $$\frac{9}{16} \div\left(-\frac{3}{4}\right)$$

Find the following sums and differences, and reduce to lowest terms. (Add or subtract as indicated.) $$\frac{1}{a}+\frac{4}{a}+\frac{5}{a}$$

Factor each of the following into a product of prime factors. $$15$$

Use the rule for order of operations to simplify each of the following. [Examples 1–3] $$\frac{3}{5}+\frac{1}{4}\left(2 \frac{1}{2}-\frac{1}{2}\right)^{3}$$

Find each of the following products. (Multiply.) $$\frac{1}{4} \cdot \frac{3}{4} \cdot \frac{3}{4}$$

Change each improper fraction to a mixed number. $$\frac{23}{5}$$

Add and subtract the following mixed numbers as indicated. \(5 \frac{4}{5}-3 \frac{1}{3}\)

Write your answers as proper fractions or mixed numbers, not as improper fractions. Find the following products. (Multiply.) $$\frac{7}{8} \cdot 6 \cdot 1 \frac{5}{6}$$

Find the quotient in each case by replacing the divisor by its reciprocal and multiplying. $$-\frac{25}{36} \div\left(-\frac{5}{6}\right)$$

Find the following sums and differences, and reduce to lowest terms. (Add or subtract as indicated.) $$\frac{5}{a}+\frac{4}{a}+\frac{3}{a}$$

Factor each of the following into a product of prime factors. $$42$$

Use the rule for order of operations to simplify each of the following. [Examples 1–3] $$2 \frac{3}{8}+\frac{1}{2}\left(\frac{1}{3}+\frac{5}{3}\right)^{3}$$

Find each of the following products. (Multiply.) $$\frac{x}{y} \cdot \frac{y}{z} \cdot \frac{z}{x}$$

Change each improper fraction to a mixed number. $$\frac{29}{6}$$

Add and subtract the following mixed numbers as indicated. \(10 \frac{5}{6}+15 \frac{3}{4}\)

Find the following quotients. $$3 \frac{1}{5} \div 4 \frac{1}{2}$$

Find the quotient in each case by replacing the divisor by its reciprocal and multiplying. $$\frac{25}{46} \div \frac{40}{69}$$

Reduce each fraction to lowest terms. $$\frac{5}{10}$$

For the set of numbers \(\left\\{\frac{3}{4}, \frac{6}{5}, \frac{12}{3}, \frac{1}{2}, \frac{9}{10}, \frac{20}{10}\right\\},\) list all the proper fractions.

Use the rule for order of operations to simplify each of the following. [Examples 1–3] $$8 \frac{2}{3}+\frac{1}{3}\left(\frac{8}{5}+\frac{7}{5}\right)^{2}$$

Find each of the following products. (Multiply.) $$\frac{y}{x} \cdot \frac{x}{z} \cdot \frac{z}{y}$$