# Adding and Subtracting Fractions

### By: Marwa and Jaymie

## Subtracting Fractions

## First Method- regular fractions

**Question: 3/5 - 2/3**

First, all you do is list the **multiples** of each **denominator**... 5,10,**15**

3,6,9,12,**15**

As you can see the **common denominator** is 15,

Now that we know the common denominator we have to multiply

5 multiplied by 3 gives us 15 and 3 multiplied by 5 gives us 15

remember anything you do to the denominator you **HAVE** to do to the **numerator**

3 x __3__ 2 x __5__

____ -- ____

5 x __3__ 3 x __5__

so our fractions are now... 9/15 - 10/15

now that we have the denominators the same we can simply subtract the numerators

9-10=1

Answer= 1/15---remember the denominator **always** stays the same.

## Second Method- improper fractions

**Question:**

**15/2 - 10/5**

First, we find the common denominator

5,**10**

2,4,6,8,**10**

As you can see 10 is the **common denominator**,now its time to multiply

5 multiplied by 2 is 10 and 2 multiplied by 5 is 10

remember anything you do to the denominator you **must** do to the numerator

15 x 5 10 x 2

_______ --- ________

2 x 5 5 x 2

our fractions are now.... 75/10 - 20/10

After that we simply subtract the numerators

75 - 20 = 55

Answer: 55/10

In this example the answer can be **reduced** and since this is a **improper fraction** we have to turn it into a **mixed number**, so we have to see how many times the denominator goes into the numerator, 10 goes into 55 , 5 times so 5 will be our **whole number **and the **remainder** is 5 and the denominator stays the same so it will be 10 so it will look like this .........

** Final Answer: 5 5/10**

**Whole #=5**

**remainder =5**

**denominator=10**

## Third Method- mixed numbers

**Question: 1 11/6 - 2 2/3**

First, we have to turn each **mixed number** into an **improper fraction**

and to do that we have first** multiply** the **whole number** and the **denominator** and then **add** the **numerator **so 1 x 6 + 11 = **17/6** and 2 x 3 + 2 =** 8/3** ---- remember the denominators **always** stay the same

Now that we have the improper fractions we must find the **common denominators **

**6**,12

3,**6**

As you can see 6 is the common denominator, 6 x 1 is 6 and 3 x 2 is 6 so...

17 x 1 8 x 2

______ ---- ______

6 x 1 3 x 2

our fractions are: 17/6 - 16/6

now that we have that we can simply subtract the numerators

17-16=1

**Answer:** 1/6