Adding and Subtracting Fractions

Adding and Subtracting Fractions

When adding or subtracting fractions with LIKE denominators you...

• Simply add the numerators together

• DO NOT add the denominators

Notice

• The top numbers were added

• The bottom number stayed the same

• If it starts the same, it will end the same (bottom number that is)

Multiple Choice

 $\frac{1}{8}+\frac{4}{8}$  

•  $\frac{5}{16}$  

•  $\frac{4}{64}$  

•  $\frac{5}{8}$  

•  $\frac{3}{8}$  

Multiple Choice

 $\frac{2}{5}+\frac{3}{5}$  

•  $\frac{5}{10}$  

•  $\frac{1}{5}$  

•  $\frac{5}{5}$  

Subtraction Works the same way

Multiple Choice

 $\frac{4}{5}-\frac{2}{5}$  

•  $\frac{6}{5}$  

•  $\frac{2}{0}$  

•  $\frac{2}{5}$  

•  $\frac{2}{10}$  

Multiple Choice

 $\frac{9}{10}-\frac{2}{10}$  

•  $\frac{7}{10}$  

•  $\frac{11}{10}$  

•  $\frac{11}{20}$  

•  $\frac{7}{0}$  

What about fractions that don't have the same denominator?

• We have to find the least common multiple (lcm)

• Or we can use the butterfly method

Finding the lcm of two numbers

• First - List the multiples of each number

• Find the lowest (least) number in common

• That number will become your new denominator

Next Steps

• Multiply each fraction by a factor that will make the denominator the lcm

• Make sure you multiply both the top and bottom by the same value!

Multiple Choice

What is the lcm of 3 and 5?

• 3

• 5

• 15

• 9

Multiple Choice

What is the lcm of 2 and 7

• 2

• 7

• 14

• 9

Multiple Choice

Rewrite this problem with common denominators

 $\frac{1}{3}+\frac{2}{5}$  

•  $\frac{1}{3}+\frac{2}{5}$  

•  $\frac{1}{3}+\frac{2}{3}$  

•  $\frac{1}{5}+\frac{2}{5}$  

•  $\frac{5}{15}+\frac{6}{15}$  

•  $\frac{1}{15}+\frac{2}{15}$  

Multiple Choice

Answer the last problem $\frac{1}{3}+\frac{2}{5}$  

•  $\frac{3}{3}$  

•  $\frac{3}{5}$  

•  $\frac{11}{15}$  

•  $\frac{3}{8}$  

Multiple Choice

 $\frac{3}{4}-\frac{2}{3}$  

•  $\frac{1}{1}$  

•  $\frac{1}{7}$  

•  $\frac{1}{12}$  

•  $\frac{1}{4}$  

•  $\frac{1}{3}$  

The butterfly method

• Multiply the denominators together

• Multiply the denominator with the numerator from the other fraction

• Add the multiplied numbers together

• 
  

• 
  

• 
  

Multiple Choice

Use the butterfly method to answer $\frac{1}{5}+\frac{2}{4}$  

•  $\frac{14}{20}$  

•  $\frac{3}{9}$  

•  $\frac{3}{20}$  

Multiple Choice

 $\frac{6}{7}-\frac{2}{5}$  

Use the butterfly method to answer

•  $\frac{4}{2}$  

•  $\frac{16}{35}$  

•  $\frac{44}{35}$  

•  $\frac{4}{35}$