When we divide fractions, we leave the first fraction unchanged (fraction on the left). We then take the reciprocal of the second fraction (fraction on the right). Once this is done, we multiply. Take the result and simplify by canceling the Greatest Common Factor from the numerator and denominator.

Test Objectives
• Demonstrate the ability to take the reciprocal of a number
• Demonstrate the ability to find the product of two fractions
• Demonstrate the ability to reduce a fraction to its lowest terms
Dividing Fractions Practice Test:

#1:

Instructions: Find each reciprocal.

a) $$\frac{7}{4}$$

b) $$\frac{2}{3}$$

c) $$-5$$

d) $$8$$

e) $$\frac{9}{14}$$

f) $$\frac{11}{13}$$

#2:

Instructions: Find each quotient.

a) $$\frac{1}{2}\hspace{.15em}÷ \hspace{.15em}\frac{1}{4}$$

b) $$\frac{2}{7}\hspace{.15em}÷ \hspace{.15em}3$$

c) $$-\frac{4}{5}\hspace{.15em}÷ \hspace{.15em}\frac{8}{9}$$

#3:

Instructions: Find each quotient.

a) $$\frac{9}{28}\hspace{.15em}÷ \hspace{.15em}\frac{12}{35}$$

b) $$\frac{8}{3}\hspace{.15em}÷ \hspace{.15em}-\frac{1}{9}$$

c) $$\frac{4}{7}\hspace{.15em}÷ \hspace{.15em}\frac{3}{14}$$

#4:

Instructions: Find each quotient.

a) $$7 \hspace{.15em}÷ \hspace{.15em}-\frac{1}{5}$$

b) $$\frac{2}{3}\hspace{.15em}÷ \hspace{.15em}10$$

c) $$\frac{5}{4}\hspace{.15em}÷ \hspace{.15em}20$$

#5:

Instructions: Find each quotient.

a) $$-\frac{1}{3}\hspace{.15em}÷ \hspace{.15em}\frac{1}{2}\hspace{.15em}÷ \hspace{.15em}\frac{2}{7}$$

b) $$\frac{5}{9}\hspace{.15em}÷ \hspace{.15em}\frac{20}{21}\hspace{.15em}÷ \hspace{.15em}\frac{3}{4}$$

Written Solutions:

#1:

Solutions:

a) $$\frac{4}{7}$$

b) $$\frac{3}{2}$$

c) $$-\frac{1}{5}$$

d) $$\frac{1}{8}$$

e) $$\frac{14}{9}$$

f) $$\frac{13}{11}$$

#2:

Solutions:

a) $$2$$

b) $$\frac{2}{21}$$

c) $$-\frac{9}{10}$$

#3:

Solutions:

a) $$\frac{15}{16}$$

b) $$-24$$

c) $$\frac{8}{3}$$

#4:

Solutions:

a) $$-35$$

b) $$\frac{1}{5}$$

c) $$\frac{1}{16}$$

#5:

Solutions:

a) $$-\frac{7}{3}$$

b) $$\frac{7}{9}$$