add/subtract/multiply/divide fractions

add/subtract/

multiply/divide fractions

Add fractions

• Step 1: find common denominators for the fractions.

• example: $\frac{1}{3}+\frac{5}{7}$  

•  $\frac{1\times7}{3\times7}+\frac{5\times5}{7\times5}$  

• You need to multiply the numerator and denominator by the same number.

• Step 2: Add or subtract the numerators(top numbers) and keep the denominator (bottom number) the same. 

•  $\frac{7}{21}+\frac{25}{21}=\frac{32}{21}$  

• step 3: If the fraction is improper, make sure to simplify it.  $\frac{32}{21}=1\frac{11}{21}$  

Multiple Choice

 $\frac{1}{4}+\frac{2}{5}$  

• 3/9

• 13/20

• 1/3

• 2/20

Multiple Choice

 $2\frac{2}{3}+4\frac{1}{8}$  

•  $6\frac{3}{11}$  

•  $6\frac{19}{24}$  

• 7

•  $6\frac{3}{4}$  

Subtracting fractions

• Step 1: Find a common denominator first like adding. If the fraction is a mixed number turn it into an improper fraction.

• Step 2: Multiply the numerator and denominator of the fraction by the same number like adding. 

• Example: $2\frac{1}{3}-1\frac{4}{5}$  

•                     $\frac{7}{3}-\frac{9}{5}$  

•             $\frac{7\times5}{3\times5}-\frac{9\times3}{5\times3}$  

•              $\frac{35}{15}-\frac{27}{15}=\frac{8}{15}$  

Multiple Choice

 $3\frac{5}{6}-2\frac{1}{2}$  

•  $2$  

•  $1\frac{4}{6}$  

•  $1\frac{1}{3}$  

• 2/3

Multiple Choice

 $\frac{7}{8}-\frac{1}{4}$  

• 5/8

• 4/8

• 6/4

• 2/3

Multiplying fractions

• Step 1: If the number is a mixed number make sure to turn it into an improper fraction.

• Step 2: Look for common factors diagonally. You should simplify the numbers if you can.

• Step 3: Multiply the numerators and multiply the denominators.

•  $3\frac{1}{3}\times2\frac{1}{5}$  

•  $\frac{10}{3}\times\frac{11}{5}$  

•  $\frac{10\div5}{3}\times\frac{11}{5\div5}=\frac{2}{3}\times\frac{11}{1}=\frac{22}{3}$  

•  $Simplify:\ 7\frac{1}{3}$  

Multiple Choice

 $\frac{4}{7}\times\frac{5}{6}$  

•  $\frac{10}{21}$  

•  $\frac{20}{42}$  

•  $\frac{11}{13}$  

• 3

Multiple Choice

 $2\frac{1}{4}\times3\frac{2}{3}$  

•  $8\frac{1}{4}$  

•  $6\frac{1}{6}$  

•  $8\frac{2}{3}$  

•  $6\frac{1}{4}$  

Dividing fractions

• Step 1: Make mixed numbers improper fractions first. If the fraction is a proper fraction just leave it alone.

• Step 2: KCF. Keep the first fraction the same, change the division to multiplication, flip the second fraction into its reciprocal.

• Step 3: multiply the same way we did before.

•  $\frac{2}{5}\div\frac{1}{7}$  

•  $\frac{2}{5}\times\frac{7}{1}$  

•  $\frac{14}{5}=2\frac{4}{5}$  

Multiple Choice

 $\frac{2}{3}\div\frac{6}{7}$  

• 14/18

• 4/7

•  $1\frac{2}{3}$  

• 7/9

Multiple Choice

 $1\frac{1}{3}\div\frac{4}{5}$  

•  $1\frac{2}{3}$  

• 2

•  $1\frac{1}{2}$  

• 4/5