Adding Fractions with Unlike Denominators

Adding Fractions with Unlike Denominators

Ways to find a common denominator

• multiply the denominators together

• find the least common multiple sometimes the LCM is one of the denominators

• Sometimes the Least Common Denominator is one of the denominators. Check to see if one of the denominators will divide into the other. If it does, that is your least common multiple

The Basics

• Numerator: Top of fraction (dividend)

• Denominator: Bottom of fraction (divisor)

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Add Fractions with Like Denominators

If denominators are the same... Add the numerators Denominator does not change

Multiple Choice

What is 1/4 + 2/4?

• 3/4

• 1/4

• 4/4 (or 1)

• 2/4

Subtract Fractions with Like Denominators

If denominators are the same, subtract the numerators

Denominator does not change

Multiple Choice

 $\frac{12}{17\ }-\frac{5}{17}$  

• 4/17

• 7/17

• 2/17

• 9/17

Why you need like denominators

1/2 + 1/4 is NOT 2/6 (or 2/4, or 2/2)

You need to obtain like denominators to add or subtract fractions

Finding common denominators (multiples)

Identify the denominators 

Write or think of the multiples for each number 

Find the Least Common Denominator

Multiple Choice

What is the Least Common Denominator?

 $\frac{1}{5}+\frac{2}{10}$  

• 5

• 10

• 15

• 20

Multiple Choice

What is the Least Common Denominator?

 $\frac{3}{4}+\frac{1}{3}$  

• 3

• 4

• 12

• 16

Remember: Unlike Denominators

Find Least Common Multiple of denominators

Multiply the numerator and denominator of each fraction by the multiple

Write the equivalent fractions

Add or subtract the numerators

Example

Multiple Choice

Solve the following practice problem. 

 $\frac{1}{5}+\frac{1}{2}$  

•  $\frac{7}{10}$ 

•  $\frac{4}{8}$  

•  $\frac{6}{7}$  

•  $\frac{8}{9}$  

Multiple Choice

Solve the following practice problem. 

 $\frac{2}{9}+\frac{1}{3}$  

•  $\frac{3}{9}$  

•  $\frac{8}{9}$  

•  $\frac{5}{9}$  

•  $\frac{3}{7}$