Fractions

1
Fractions

• Simplest Form

2
Equivalent Fractions

• There can be more than one fraction that
  represents the same value.
• 2/3 4/6 8/12

3
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.

4
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.

5
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 ?

6
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
7
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
8
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.

9
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