Adding and Subtracting Fractions

Adding and Subtracting Fractions

Use your mini lessons as you go through this activity.

Least Common Multiple (LCM)

Look for the smallest multiple two numbers have in common.

Example: 6 , 8

Multiples of 6: 6, 12, 18, 24, 30, 36, 42

Multiples of 8: 8, 16, 24, 32, 40, 48, 56

The smallest multiple that the two numbers share is 24.

To save time, start finding the multiples of the larger number first it is easier to see what the lowest value is by beginning big.

Find the LCM of 18 and 12

• Begin with 18 (multiples of 18) 18, 36, 54, 72

• Now that you have those listed can you see a multiple of 12 that is common between them?

• 36 is the common multiple.

Multiple Choice

Find the LCM for 40 and 10

• 20

• 80

• 40

Writing fractions with the LCD as a denominator (Least Common Denominator)

• Use what you have learned about LCM

• Example: Find the LCD for  $\frac{3}{20}$   and  $\frac{1}{5}$  .

• Find the LCM for 20 and 5.  Start with 20 (multiple of 20) 20, 40, 60

• Multiples of 5: 5, 10, 15, 20.
  
  

• The LCM is 20.  Use this as the LCD to change the denominators so they are the same value.

• Remember we bumped fractions so they were equivalent.  This is where this takes place.

•  $\frac{3}{20}$  does not have to be changed however,  $\frac{1}{5}$  will need to be changed to a denominator of 20.

Making the denominator equivalent

 $\frac{1}{5}$  = $\frac{x}{20}$  4 is the multiple that bumped this denominator so the numerator is now multiplied by the 4.  The equivalent fraction is  $\frac{4}{20.}$  

Multiple Choice

You try: Find the LCD for

 $\frac{1}{8}\ and\ \frac{2}{6}$  

• LCD is 12

• LCD is 48

• LCD is 36

• LCD is 24

Comparing Fractions

• When you have to compare fractions the denominators need to be the same.

• You need to use what we just learned about finding the LCD and making both denominators the same to compare them.

• Example: Which fraction is larger?

   $\frac{3}{17}\ or\ \frac{2}{17}$  

• Because both of the denominators are the same we compare the numerators to answer the question.   $\frac{3}{17}$   is the larger fraction.

Comparing Fractions

• Which is larger?

   $\frac{1}{5}$  or  $\frac{2}{9}$  

• First find the LCD between 5 and 9.  That means what is the least common multiple between them.  45 is the LCM so that will be the LCD.

• Now bump both fractions to have the LCD of 45.   $\frac{1}{5}\ =\ \frac{9}{45}$  and  $\frac{2}{9}\ =\ \frac{10}{45}$  

• Can you answer the question now?  Both of the denominators are equivalent so you can see which is larger by comparing the numerators.

Multiple Choice

Which is larger

 $\frac{2}{3}\ or\ \frac{1}{2}$  ? Use > or < to show which is greater.

• >

• <

Addition and subtraction of fractions

• When adding and subtracting fractions the denominators must be the same.

• Add only the numerators leaving the denominator the same when solving the problem.

• Example:        $\frac{2}{5}\ +\ \frac{1}{5}\ =\ \frac{3}{5}$  

  
  

• Subtract only the numerators leaving the denominator the same when solving the problem.

• Example:   $\frac{7}{8}\ -\ \frac{3}{8}\ =\ \frac{4}{8}$  

• Notice the denominator does not change.  The numerator is the only value that will do the operation.

Multiple Choice

Subtract:

 $\frac{14}{15}\ -\ \frac{11}{15}$  

•  $\frac{3}{0}$  

•  $\frac{3}{15}$  

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