Question

mixed review
how to add fractions
how to multiply fractions
$\frac{1}{5}+\frac{3}{5}$
$\frac{7 cdot 1}{7 cdot 2}+\frac{3 cdot 2}{7 cdot 2}$
$\frac{1}{2} \times \frac{3}{4}$
$\frac{3}{8} \times 2$
$3 \frac{1}{5} \times 4 \frac{1}{6}$
$\frac{1 + 3}{5}=\frac{4}{5}$
$\frac{7 + 6}{14}=\frac{13}{14}$
$\frac{1}{2} \times \frac{3}{4}=\frac{1 cdot 3}{2 cdot 4}$
$\frac{3}{8} \times \frac{2}{1}=\frac{3 cdot 2}{8 cdot 1}=\frac{6}{8}$
$\frac{21}{5} \times \frac{25}{3}=\frac{21 cdot 25}{5 cdot 3}=\frac{525}{15}$
$=\frac{3}{8}$
$=\frac{3}{4}$
$=15 \frac{2}{5}$
how to divide fractions
by fractions
by whole numbers
by mixed numbers
$\frac{2}{3} div \frac{4}{5}$
$\frac{3}{7} div 2$
$6 \frac{1}{2} div 2 \frac{1}{4}$
$\frac{2}{3} div \frac{4}{5}=\frac{2}{3} \times \frac{5}{4}$
$\frac{3}{7} div \frac{2}{1}=\frac{3}{7} \times \frac{1}{2}$
$\frac{13}{2} div \frac{9}{4}=\frac{13}{2} \times \frac{4}{9}$
$\frac{2}{3} \times \frac{5}{4}=\frac{2 cdot 5}{3 cdot 4}=\frac{10}{12}=\frac{5}{6}$
$\frac{3}{7} \times \frac{1}{2}=\frac{3 cdot 1}{7 cdot 2}=\frac{3}{14}$
$\frac{13}{2} \times \frac{4}{9}=\frac{13 cdot 4}{2 cdot 9}=\frac{52}{18}=\frac{26}{9}=2 \frac{8}{9}$
directions: show all work.

1. $\frac{7}{8}+\frac{3}{4}$
2. $6 \times 1 \frac{1}{9}$
3. $5 \frac{2}{7}+3 \frac{5}{9}$
4. $\frac{5}{6}+\frac{1}{2}$
5. $\frac{2 \frac{1}{4}}{1 \frac{1}{8}}$

Explanation:

Step1: Find common denominator

$\frac{7}{8} + \frac{3}{4} = \frac{7}{8} + \frac{6}{8}$

Step2: Add numerators

$\frac{7+6}{8} = \frac{13}{8}$

Step1: Convert to improper fractions

$5\frac{2}{7} + 3\frac{5}{6} = \frac{37}{7} + \frac{23}{6}$

Step2: Find common denominator

$\frac{37\times6}{7\times6} + \frac{23\times7}{6\times7} = \frac{222}{42} + \frac{161}{42}$

Step3: Add numerators

$\frac{222+161}{42} = \frac{383}{42}$

Step1: Convert to improper fraction

$6 \times 1\frac{1}{9} = 6 \times \frac{10}{9}$

Step2: Multiply and simplify

$\frac{6\times10}{9} = \frac{60}{9} = \frac{20}{3}$

Step1: Rewrite as multiplication

$\frac{5}{6} \div \frac{1}{2} = \frac{5}{6} \times \frac{2}{1}$

Step2: Multiply and simplify

$\frac{5\times2}{6\times1} = \frac{10}{6} = \frac{5}{3}$

Step1: Convert to improper fractions

$\frac{2\frac{1}{4}}{1\frac{1}{2}} = \frac{\frac{9}{4}}{\frac{3}{2}}$

Step2: Rewrite as multiplication

$\frac{9}{4} \times \frac{2}{3}$

Step3: Multiply and simplify

$\frac{9\times2}{4\times3} = \frac{18}{12} = \frac{3}{2}$

Answer:

1. $\frac{13}{8}$
2. $\frac{383}{42}$
3. $\frac{20}{3}$
4. $\frac{5}{3}$
5. $\frac{3}{2}$