Dividing Fractions by Fractions

To Divide Fractions:

• Invert (i.e. turn over) the denominator fraction and multiply the fractions
• Multiply the numerators of the fractions
• Multiply the denominators of the fractions
• Place the product of the numerators over the product of the denominators
• Simplify the Fraction

Example: Divide 2/9 and 3/12

• Invert the denominator fraction and multiply (2/9 ÷ 3/12 = 2/9 * 12/3)
• Multiply the numerators (2*12=24)
• Multiply the denominators (9*3=27)
• Place the product of the numerators over the product of the denominators (24/27)
• Simplify the Fraction (24/27 = 8/9)
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• The Easy Way. After inverting, it is often simplest to "cancel" before doing the multiplication. Canceling is dividing one factor of the numerator and one factor of the denominator by the same number.
• For example: 2/9 ÷ 3/12 = 2/9*12/3 = (2*12)/(9*3) = (2*4)/(3*3) = 8/9