Adding and Subtracting Fractions with Uncommon Denominators

Add/Subtract Like Fractions

REVIEW

Multiple Choice

When adding/subtracting like fractions. What do you do with the denominator?

• Find a common denominator

• Add the denominators

• Multiply the denominators

• Keep the denominator

Remember:

If the we're adding/subtracting like denominators, that means the denominators are already in common. So we don't have to do anything to the denominators in this situation.

Multiple Choice

Try it on your own. (Don't forget the rules of adding and subtracting with negative numbers!)


$$\frac{-3}{8}-\frac{1}{8}$$  

• $$\frac{-4}{8}=-\frac{1}{2}$$  

• $$\frac{-2}{8}=-\frac{1}{4}$$  

• $$\frac{-4}{16}=-\frac{1}{4}$$  

• $$\frac{-2}{16}=-\frac{1}{8}$$  

Multiple Choice

When adding/subtracting negative fractions, it's best to put the negative sign with the numerator.

• True

• False

Remember:

When adding/subtracting like fractions, you keep the denominator the same and you add/subtract the numerators. So, if a fraction is negative, it is helpful to put the negative sign next to the numerator to avoid any mistakes with our negative signs. 

Example:

 $-\frac{1}{7}+-\frac{1}{7}=\frac{-1}{7}+\frac{-1}{7}$  

 $=\frac{-2}{7}$  

Multiple Choice

If your answer to a problem is a negative fraction, you need to put the negative...

• out if front of the fraction, like this: $$-\frac{2}{7}$$  

  
  

• in the numerator, like this: $$\frac{-2}{7}$$  

• in the denominator, like this:  $$\frac{2}{-7}$$  

• All three options are equivalent and acceptable. But the first option is most common. 

Remember:

Every fraction is a division problem. And if there is an odd number of negative signs (in the previous example's case, there was 1 negative sign), then the answer is negative. So, if a fraction is negative, you can put that ONE negative sign out in front, on top, or on bottom.

Time to practice:

Don't Forget:

Addition:

1) Same signs add/keep the sign

2) Different signs subtract/keep the larger

Subtraction:

1) Keep, Change, Change

2) Follow the rules of addition above

Fractions: Simplify when possible

Multiple Choice

Add -7/10 + (-4/10). Simplify if necessary.

• -1 1/10

• -11/10

• 1/10

• 1 1/10

Multiple Choice

1/8 - 7/8. Simplify if necessary.

• 6/8

• -6/8

• 3/4

• -3/4

Multiple Choice

(-5/9) - 2/9

• -7/9

• 7/9

• 2/3

• 3/4

Multiple Choice

(-4/5) - (-1/5)

• -3/5

• 3/5

• 1/3

• 2/5

Multiple Choice

(-1/9) + (-5/9)

• 6/9

• -2/3

• 2/3

• 1/3

Multiple Choice

3/8 + (-7/8)

• 1/2

• -1/2

• 4/8

• -4/8

Multiple Choice

(-11/12) - (-5/12)

• -1/2

• 1/2

• 6/12

• -6/12