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Fractions

- Simplest Form

Equivalent Fractions

- There can be more than one fraction that

represents the same value. - 2/3 4/6 8/12

Fractions in Simplest Form

- A fraction is in simplest form when it can no

longer be reduced, - or
- its numerator and denominator have the greatest

common factor of 1.

Reducing Fractions

- One strategy to use for reducing fractions is to

use the divisibility tests. - If the numerator and denominator both pass the

same divisibility test, then it can be reduced by

that number.

Divisibility Tests

- 2 Is the number an even number ?
- 3 Do all the digits add up to a number

divisible by 3 ? - 4 Is the number made by the last two digits

divisible by 4 ? - 5 Is the ones digit a 5 or 0 ?
- 6 Is the number even and divisible by 3 ?
- 9 Do all the digits add up to a number

divisible by 9 ? - 10 Is the ones digit a 0 ?

Divisibility Test Method

- 14/16

The numerator and denominator are both even

numbers.

7/8

So it can be reduced by 2

The numerator and denominator both pass the 3

divisibility test.

9/21

3/7

So it can be reduced by 3

Divisibility Tests Cont.

- Sometimes you may have to use the divisibility

test more than one time to get to the simplest

form of the fraction.

27/36

The 3 divisibility test works with this fraction.

9/12

The 3 divisibility test will work again on this

fraction.

3/4

Factoring Method

- Find and list all the factors for the numerator.
- Find and list all the factors for the

denominator. - Identify what the Greatest Common Factor is.
- Divide both the numerator and denominator by this

Greatest Common Factor.

Factoring Method Cont.

- 12/18

Factors of 18 1 x 18 2 x 9 3 x 6 6 x 3 1

, 2 , 3 , 6 , 18

Factors of 12 1 x 12 2 x 6 3 x 4 4 x 3 1

, 2 , 3 , 4 , 6 , 12

12 6

2

or 2/3

18 6

3