**Operations with Fractions**

by Hamish Reed

by Hamish Reed

**What Are Fractions?**

Multiplying Fractions

When multiplying fractions, you simply multiply the numerators and the denominators with each other:

Dividing fractions

To divide fractions, you multiply them by the reciprocal fraction:

Adding and Subtracting Fractions

**Adding and Subtracting Fractions with**

Different Denominators

Different Denominators

First thing to do is find the

common denominator

and

keep the value of the fraction the same.

You do this is by multiplying the denominator's together. You then multiply the numerator's by the denominator's add or subtract their product together and you've got your answer!

At it's most basic conceptual level, a fraction is part of a whole.

If you have a pizza would you rather have 4/6 or 6/8 of the pizza?

4/6 of the pizza is the same as 8/12 of the pizza

6/8 of the pizza is equivalent to 9/12 of the pizza

...so what would you rather have, 4/6 or 6/8 of the pizza?

Fractions help us figure this out!

The Fraction

Fraction bar

Numerator

Denominator

By Hamish

If you add or subtract fractions together with the same denominator, the answer will have the same denominator.

To find the total, just add or subtract the two numerators together:

The reciprocal of a fraction

The reciprocal is the opposite of a fraction: 6/5

is the reciprocal of

5/6

3/4 + 2/4 = 5/4 = 1 1/4

for example:

3/4/ + 1/4 = 4/4 = 1

7/8 + 2/5

(7 x 5) + (2 x 8)

(5 x 8)

35 + 16 = 51

40 40

This method is known as:

criss cross applesauce!

You can simplify your fractions if both the numerator and the denominator can be divided by the

same number

... for example:

With the fraction 20/35, both 20 and 35 are divisible by 5 so your simplified fraction with an equal value to 20/35 is 4/7.

2 x 1 = (2 x 1) = 2 don't forget to simplify!

3 2 (3 x 2) 6

2 = 1

6 3

6/9 ÷ 8/12

6 ÷ 8 = 6 × 12 = 6 × 12 = 72 = 1

9 12 9 8 9 × 8 72

7 - 6

12 13

7 x 13 - 6 x 12

12 x 13 13 x 12

91 - 72 = 19

156 156

13 - 9 = 13 - 9 = 4 = 1

24 24 24 24 6

Find the Common Denominator:

in this example the common denominator is

12 x 13

remember: criss cross applesauce!