Multiplication and Division of Fractions
Reciprocals
- Also known as the multiplicative inverse. - Inverse of a fraction. - Any number multiplied by its reciprocal equals 1. - Example: 1/6 x 6/1 = 1
Dividing a Whole Number by a Mixed Number
- Change any mixed number to improper fractions - Take reciprocal (invert/turn upside down) the second fraction (the one "divided by") - Multiply Fractions - Reduce to lowest term - Example: 15 divide 1 2/3 = ? 15 divide 1 2/3 = 15/1 divide 5/3 = ? 15/1 divide 5/3 = 15/1 x 3/5 = 45/5 = 9
Dividing a Fraction by a Whole or Mixed Number
- Change any mixed number to improper fractions - Take reciprocal (invert/turn upside down) the second fraction (the one "divided by") - Multiply Fractions - Reduce to lowest term - Example: 2/3 divide 5 = ? 2/3 x 1/5 = 2/15
Dividing a Whole or Mixed Number by a Fraction
- Change any mixed number to improper fractions - Take reciprocal (invert/turn upside down) the second fraction (the one "divided by") - Multiply Fractions - Reduce to lowest term - Example: 3 divide 2/3 = ? 3/1 x 3/2 = 9/2 = 4 1/2
Divide a Mixed Number by a Whole Number
- Change any mixed number to improper fractions - Take reciprocal (invert/turn upside down) the second fraction (the one "divided by") - Multiply Fractions - Reduce to lowest term - Example: 5 1/3 divide 8 = ? 16/3 divide 8/1 = 16/3 x 1/8 = 16/24 = 2/3
Multiply Mixed Numbers
- Operation: - Convert mixed number to an improper fraction - Multiply numerators - Multiply denominators - Reduce answer to lowest term - Example: 3 1/3 x 2 1/4 = ? 3 1/3 x 2 1/4 = 10/3 x 9/4 = ? 10/3 x 9/4 = 90/12 = 7 6/12 = 7 1/2
Multiply a Fraction by a Whole or Mixed Number
- Operation: - Multiply the numerators - Multiply the denominators - Reduce answer to lowest term - Example: 2/3 x 1/5 x 3/6 = 6/90 = 1/15
Multiplying a Fraction by a Whole or Mixed Number
- Operation: - Rewrite whole or mixed numbers to improper fractions. - Multiply the numerators and multiply the denominators together. - Reduce answer to lowest term - Example: 2/3 x 6 = ? 2/3 x 6/1 = 12/3 = 4
Dividing a Fraction by a Fraction
- Take reciprocal (invert/turn upside down) the second fraction (the one "divided by") - Multiply Fractions - Reduce to lowest term - Example: 1/2 divide 2/3 = ? - Multiply 1/2 by reciprocal of 2/3 - 1/2 x 3/2 = 3/4
