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Dividing Fractions By: Greg Stark

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Division A basic rule of math – if you multiply the dividend (the number being divided) and the divisor (the number you are dividing by) by the same factor, the answer will not change 4 2 2 ÷ = 4 2 = 8 4 2 ÷ ÷ = X 2 X 2 4 2 = 20 10 2 ÷ ÷ = X 5 X 5

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Division What is the easiest number to divide by? A basis rule of math – dividing by 1 does not change the value of number 4 1 4 ÷ = 2 1 2 ÷ = 326 1 326 ÷ =

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**3 1 3 Division by a Fraction ÷ ÷ ÷ = ÷ = 3 4 1 4 3 4 4 1 \ 1 4 4 1 \ x**

How can we use this information to divide by one? A basic rule of math – if we multiply a number by it’s inverse, the product is one 1 1 3 4 1 4 3 4 4 1 \ 1 4 4 1 \ ÷ ÷ 4 ÷ ÷ 4 x x \ \ ÷ 4 ÷ 4 1 1 1 3 1 1 3 1 ÷ 3 = ÷ = 2 3

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**Dividing a Fraction by a Fraction**

Another example: 1 1 1 2 3 2 7 2 3 \ 7 2 2 7 \ 7 2 \ ÷ ÷ 2 ÷ ÷ 2 ÷ 7 x x \ \ \ ÷ 2 ÷ 7 ÷ 2 1 1 1 7 3 1 3 2 =

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**Dividing a Whole Number by a Fraction**

For example: 1 1 2 5 1 2 1 1 2 2 1 \ 5 ÷ ÷ ÷ 2 x x \ ÷ 2 1 10 1 10 =

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**Dividing Mixed Numbers**

In order to divide with fractions, both factors must be in the form of fractions To convert a mixed number into a fraction, multiply the whole number by the denominator of the fraction, then add the product to the numerator 1 5 2 3 13 25 21 5 5 3 21 5 3 5 63 25 4 ÷ 1 2 = ÷ x = = =

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**Review: Dividing with fractions**

Ensure all values are fractions, before you beginning the division process To convert a whole number to a fraction, place it over 1. To convert a mixed number to a fraction, multiply the whole number by the denominator of the fraction, then add the product to the numerator Invert the divisor - the fraction you are dividing by – and multiply the fractions together Reduce the product to lowest terms

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