Question

unit 4 dividing fractions: end of unit study guide
for all questions: write your answer(s) on the line. all work must be shown to receive full credit.

1. find the area of the rectangle in which the base is 10 inches, and the height is $3\frac{1}{5}$ inches.

multiply. show all of your work. simplify, if necessary.

1. $\frac{4}{5}\cdot\frac{3}{4}$
2. $\frac{3}{7}\cdot1\frac{2}{3}$

divide. show all of your work. simplify, if necessary.

1. $\frac{4}{6}\div\frac{2}{9}$
2. $\frac{9}{2}\div\frac{9}{12}$
3. $\frac{5}{12}\div\frac{2}{10}$
4. $2\frac{6}{7}\div\frac{5}{9}$

Explanation:

Step1: Convert mixed number to fraction

$3\frac{1}{5} = \frac{3\times5 + 1}{5} = \frac{16}{5}$

Step2: Calculate rectangle area

$\text{Área} = 10 \times \frac{16}{5} = \frac{10\times16}{5} = 32$

Step3: Multiply fractions (Pregunta 2)

$\frac{4}{5} \cdot \frac{3}{4} = \frac{4\times3}{5\times4} = \frac{3}{5}$

Step4: Convert mixed number, multiply

$1\frac{2}{3} = \frac{5}{3}$, $\frac{3}{7} \cdot \frac{5}{3} = \frac{3\times5}{7\times3} = \frac{5}{7}$

Step5: Rewrite division as multiplication

$\frac{4}{6} \div \frac{2}{9} = \frac{4}{6} \cdot \frac{9}{2}$

Step6: Simplify and calculate

$\frac{4\times9}{6\times2} = \frac{36}{12} = 3$

Step7: Rewrite division, simplify

$\frac{9}{2} \div \frac{9}{12} = \frac{9}{2} \cdot \frac{12}{9} = \frac{12}{2} = 6$

Step8: Rewrite division, simplify

$\frac{5}{12} \div \frac{2}{10} = \frac{5}{12} \cdot \frac{10}{2} = \frac{5\times10}{12\times2} = \frac{50}{24} = \frac{25}{12} = 2\frac{1}{12}$

Step9: Convert mixed number, divide

$2\frac{6}{7} = \frac{20}{7}$, $\frac{20}{7} \div \frac{5}{9} = \frac{20}{7} \cdot \frac{9}{5} = \frac{20\times9}{7\times5} = \frac{180}{35} = \frac{36}{7} = 5\frac{1}{7}$

Answer:

1. 32 square inches
2. $\frac{3}{5}$
3. $\frac{5}{7}$
4. $3$
5. $6$
6. $2\frac{1}{12}$ o $\frac{25}{12}$
7. $5\frac{1}{7}$ o $\frac{36}{7}$