Student Learning Centre Rules for fractions ADDITION AND SUBTRACTION To add or subtract fractions they must have the same denominator (the bottom value).

Addition and Subtraction with the same denominators If the denominators are already the same then it is just a matter of either adding or subtracting the numerators (the top value).

Example + = = = Addition + 3 2 3+2 5 𝐴𝐴 𝐶𝐶 𝐴𝐴+𝐶𝐶 4 4 4 4 𝐵𝐵 𝐵𝐵 𝐵𝐵 Subtraction = Example = = 𝐴𝐴 𝐶𝐶 𝐴𝐴−𝐶𝐶 3 2 3−2 1 Addition and Subtraction𝐵𝐵 − 𝐵𝐵with d𝐵𝐵ifferent denominators 4 − 4 4 4 If the denominators are different then a common denominator needs to be found. This is most easily done by creating a common denominator that is the product of the two differing denominators. To achieve this multiply the denominator and the numerator of each fraction by the opposite denominator. This is actually the same as multiplying 1 and so we aren’t really changing anything.

( ) ( ) + = + = Example + = + = = Addition ( ) ( ) 𝐴𝐴 𝐶𝐶 𝐴𝐴𝐴𝐴 𝐵𝐵𝐵𝐵 𝐴𝐴𝐴𝐴+𝐵𝐵𝐵𝐵 3 2 3 3 2 5 9+10 19 𝐵𝐵 𝐷𝐷 𝐵𝐵𝐵𝐵 𝐵𝐵𝐵𝐵 𝐵𝐵𝐵𝐵 5 3 5 3 3 5 15 15

Subtraction = = Example = = = 𝐴𝐴 𝐶𝐶 𝐴𝐴𝐴𝐴 𝐵𝐵𝐵𝐵 𝐴𝐴𝐴𝐴−𝐵𝐵𝐵𝐵 2 3 2 5 3 3 10−9 1 𝐵𝐵 − 𝐷𝐷 𝐵𝐵𝐵𝐵 − 𝐵𝐵𝐵𝐵 𝐵𝐵𝐵𝐵 3 − 5 3 5 − 5 3 15 15 MULTIPLICATION

To multiply fractions simply multiply the nominators × = Example: × = = and multiply the denominators: a 𝐴𝐴 𝐶𝐶 𝐴𝐴𝐴𝐴 4 2 8 4 𝐵𝐵 𝐷𝐷 𝐵𝐵𝐷𝐷 7 6 42 21 DIVISION

To divide one fraction by another we must flip the ÷ = × = Example: ÷ = × = = second fraction and then multiply with the first: 𝐴𝐴 𝐶𝐶 𝐴𝐴 𝐷𝐷 𝐴𝐴𝐷𝐷 2 4 2 7 14 7 𝐵𝐵 𝐷𝐷 𝐵𝐵 𝐶𝐶 𝐵𝐵𝐶𝐶 3 7 3 4 12 6 PRACTICE

1) + = 2) × = 2 4 3 5 7 3 4 6

3) ÷ = 4) = 7 2 7 3 12 3 12 − 8 Check your answers on the back. Rules of Fractions 5/2013 @ SLC 1 of 2

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