# Adding and Subtracting Fractions

### This is a Study sheet to help you practise and review

## Adding Fractions

## adding improper fractions

## Subtracting Fractions

## Subtracting Basic Fractions

__Equation__: 2/5 - 3/10

__Explanation:__

To do this equation start by finding a common denominator to do that you can list the multiples or multiply the two denominator and the common denominator would be 10. Now whatever you did to each denominator to get 10 do that to the numerators as well. So in the first fraction you need to do 5 x 2 to get 10 so now you have to multiply the numerator with two as well, 2 x 2=4. Since in the second fraction the denominator is already at 10 you don't need to do anything to it, but if it wasn't you would multiply the numerator with whatever you multiplied the denominator with. So now the equation is 4/10 - 3/10. Now subtract the numerators but keep the denominator the same. So 4-3=1 and the final answer is 1/10

__Steps:__

1. Find the common denominator preferably the lowest common denominator

2. Whatever you did to the denominators of each fraction to get the common denominator do to the numerators as well

3. Subtract the numerators, and keep the denominators the same

4. Simplify if needed

__Numbers:__

2/5 - 3/10 ~equation

= 4/10 - 3/10 ~common denominators

=1/10 ~numerators subtracted, final answer

## The subtracting part starts at 2:40

Practice makes perfect

## Subtracting Improper fractions

__Equation__: 4/2 - 4/3

__Explanation:__

To do this equation start by finding the common denominator to do that you can list the multiples of the denominators until you find a common one or you can multiply the denominators together. In this case the common denominator is 6. Next whatever you did to the denominator of each fraction, do to the numerator as well. So since I had to multiply the denominator of the first fraction by 3 I need to multiply the numerator with 3 as well, 4 x 3=12. Now do that to the other fraction too. So to get six I need to multiply the second denominator by 2, so I have to multiply the numerator with 2 as well, 4 x 2=8. Now the fractions are 12/6 - 8/6. The next step is to subtract the numerators as normal, and keep the denominators the same. So 12-8=4 so the answer would be 4/6. You can still go further by simplifying the fraction so 4/6=2/3. If by the end the fraction is still improper you should turn it back into a mixed number. To do that you need to ask yourself how many times the denominator goes into the numerator, the number of times that is, is the whole number. The leftover is the numerator and the denominator stays the same

__Steps:__

1. Find the common denominator

2. Whatever you did to the denominator do to the numerator as well

3. subtract the numerators

4. if still improper convert to a mixed number

5. Simplify if needed

Numbers:

4/2 - 4/3

= 12/6 - 8/6 ~common denominator

= 4/6 ~subtracted denominator

= 2/3 ~simplified

## Different ways to find common denominators

## Listing multiples can be less efficient | ## Multiply denominators may require you to simplify at the end | ## Think If your good at mental math this is the strategy for you |

try your best

## Subtracting mixed fractions

__Explanation:__

To subtract mixed numbers start by turning the mixed numbers into improper fractions. To do that you need to multiply the whole number by the denominator then add the numerator. So for the first fraction the improper fraction would be 3 x 3+2=11 and for the second fraction the improper fraction would be 1 x 5+2=7. You would keep the denominator the same. So the equation is 11/3 - 7/5. Next I'm going to find the common denominator to do that I am going to multiply the two denominators which give me 15. Now whatever I needed to do to each fraction's denominator to get 15 do that to the numerator as well. For the first fraction I need to multiply the denominator by 5 so I have to multiply the numerator as well, 11 x 5=55. Now do that to the other fraction as well so 5 x 3=15, the numerator 7 x 3= 21. So the fractions are 55/15 and 21/15. Now subtract the numerators 55-21=34 and the denominator stays the same so the answer is 34/15. But since the equation is in mixed numbers the answer should be in mixed numbers too. So to convert the improper fraction I need to ask myself how many times the denominator goes into the numerator, 15 goes into 34 two times. So the whole number is two the leftover is the numerator and the denominator stays the same. So the answer is 2 4/15. If you can reduce it then simplify it

__Steps:__

1. Convert mixed numbers to improper fractions

2. Find a common denominator (look above for the different ways to find the common denominator)

3. whatever you did to the denominator of each fraction do to the numerator as well

4. Subtract the numerators

5. Turn improper fraction back into mixed (# of times denominator goes into numerator leftover in the numerator and denominator stays the same)

6. Simplify if needed

__Numbers:__

3 2/3 - 1 2/5 ~equation

=11/3 - 7/5 ~improper to mixed

=55/15 - 21/15 ~common denominator

= 34/15 ~numerators subtracted

= 2 4/15 ~mixed number final answer

## Picture method learn better with pictures? then this example is for you | ## Number Method learn better with numbers? then this example is for you | ## Improper fraction to Mixed Number Need some more help converting? look at this |

has some addintion ones to