Add and Subtract Fractions with Unlike Denominators

Add and Subtract Fractions with Unlike Denominators

Anthony rode his electric scooter 1/2 mile from his house to the park. Later he rode 1/3 mile from the park to baseball practice. How far did Anthony ride?

Which operation are we going to do and how do you know?

Multiple Choice

The first step when adding or subtracting fractions is to ...

• Add the numerators

• Make sure the numerators are the same

• Make sure the denominators are the same

• Add the denominators together

Step 1 Since the denominators for 1/2 and 1/3 are not the same. change the fractions to equivalent fractions with a common, or like, denominator.

• Which means finding the least common multiple

Multiple Choice

What is the least common multiple of

 $\frac{1}{2}$  and  $\frac{1}{3}$  

• 1

• 5

• 6

• 12

What do we do once we find a common denominator?

*Multiply the fractions by a WHOLE fraction (like 2/2 or 4/4 or 6/6) to change them to fractions with our common denominator without changing the value or amount. (Multiplying by 1 doesn't change the amount, right?)

*Use the new fractions with the same denominator to add or subtract the numerators!

Step 2 Make the equivalent fractions.

Since the common multiple was 6, you will need to change both denominators to 6.

1/2 x 3/3= 3/6

Multiple Choice

  $\frac{1}{3}$  =  $\frac{?}{6}$  

•  $\frac{4}{6}$  because  $\frac{1}{3}$  +  $\frac{3}{3}$  =  $\frac{4}{6}$  

•  $\frac{2}{6}$  because  $\frac{1}{3}$  x  $\frac{2}{2}$  = $\frac{2}{6}$  

Step 3 Add the numerators. Simplify if necessary. The denominator stays the same.

 $\frac{1}{2}$  = $\frac{3}{6}$  

 $\frac{1}{3}$  =  $\frac{2}{6}$  

so  $\frac{3}{6}$  +  $\frac{2}{6}$  = $\frac{5}{6}$  

Anthony rode his electric scooter  $\frac{5}{6}$   mile.

Multiple Choice

To make grape juice, Elizabeth added  $\frac{5}{8}$  cup of water to  $\frac{1}{4}$  cup of grape juice concentrate. How much grape juice did Elizabeth make? Before solving, what is the least common multiple?

• 9

• 16

• 12

• 8

Multiple Choice

To make grape juice, Elizabeth added  $\frac{5}{8}$  cup of water to  $\frac{1}{4}$  cup of grape juice concentrate. How much grape juice did Elizabeth make?

•  $\frac{14}{16}$  because  $\frac{5}{8}$  x $\frac{2}{2}$  = $\frac{7}{16}$  and  $\frac{1}{4}$  x $\frac{4}{4}$  = $\frac{5}{16}$  so   $\frac{7}{16}$  + $\frac{5}{16}$  = $\frac{12}{16}$  

•   $\frac{7}{8}$  because  $\frac{1}{4}$  x $\frac{2}{2}$  = $\frac{2}{8}$  so  $\frac{5}{8}$  + $\frac{2}{8}$  = $\frac{7}{8}$  

Multiple Choice

Can  $\frac{7}{8}$  be simplified?

• Yes

• No

Multiple Choice

What would you multiply 2/3 by the rename it with the denominator 12?

• $\frac{3}{3}$

• $\frac{4}{4}$

• $\frac{2}{2}$

• $\frac{12}{12}$

What happens if we are subtracting fractions with unlike denominators?

It works the same as adding fractions with unlike denominators.

Multiple Choice

 $\frac{2}{5}$  - $\frac{1}{3}$  

Rewrite this problem with common denominators

•  $\frac{2}{5}$  - $\frac{3}{5}$  

•  $\frac{2}{15}$  + $\frac{1}{15}$  

•  $\frac{6}{15}$  - $\frac{5}{15}$  

•  $\frac{2}{5}$  - $\frac{1}{3}$  

Multiple Choice

A  $\frac{1}{2}$  yard length of yarn is needed for a Valentine's 

Day craft project. If this yarn length is cut, how much yarn will remain from a piece that measures  $\frac{7}{8}$  yard?

•  $\frac{3}{16}$  yard

•  $\frac{1}{4}$  yard

•  $\frac{1}{6}$  yard

•  $\frac{3}{8}$  yard