6th Grade - Multiplication and Division of Fractions

Introduction

  • "Fraction" represents a relation of a part(s) to the whole, where the whole is divided into equal parts. 
  • Fraction = numeratordenominator= part(s)whole
  • Any whole number can be written as a fraction. For example: 5 = 51. This is helpful when multiplying and dividing fractions.
  • 23 is a Proper Fraction (the denominator is greater than the numerator).
  • 53 is an Improper Fraction (the numerator is greater than the denominator).
  • 123 is a Mixed Number/Fraction (whole number + proper fraction).

Multiplication of Fractions/Mixed Numbers

  • To multiply fractions/mixed numbers.
    1. Convert the mixed numbers into an improper fraction. 
    2. Multiply the numerators.
    3. Multiply the denominators. 
    4. Simplify to the lowest (simplest) term.
  • Occasionally, fractions can be simplified before multiplying.

Example 1: solve: 34·25

Solution: 34·25=3 × 24 × 5

           =620   (simplify the fraction to its lowest terms.)

           =6 ÷ 220 ÷ 2

           =310

Example 2: A recipe needs 213cups of sugar for a loaf of banana bread. Ms. Suzy wants to cut the sugar in half. How much sugar will Ms. Suzy use for the banana bread?  

Solution: Convert the mixed number to a proper fraction. 

213  = 2+1×3 = 73

Ms. Suzy cuts the sugar in half.

= 73 × 12

=76

Change improper fraction to a mixed number by dividing the numerator by the denominator.

 = 116           

Ms. Suzy uses 116cups of sugar to make a loaf of banana bread. 

Division of Fractions/Mixed Numbers

  • Fractions can be divided by changing them into multiplication.
  • Each division expression can be written as a multiplication expression by applying the rule " Keep, Change & Flip." This rule works from left to right.
  • Keep, Change, & Flip rule

1. Keep the first fraction of the expression the same.

2. Change the division sign to multiplication.

3. Flip the last fraction.

   Example: 13 ÷25

   =13 × 52

  • To divide fractions/mixed numbers.
    1. Convert each mixed number into an improper fraction. 
    2. Convert the division expression to multiplication by following the rule "Keep, Change, & flip ."
    3. Multiply the numerators.
    4. Multiply the denominators.
    5. Simplify to the lowest (simplest) form.

Example1: Solve 12÷2.

Solution:  12÷ 2 

= 12 ÷ 21

Change division to multiplication by applying the "Keep, Change, & Flip" rule.

=12×12

 Multiply across the numerators and denominators.

 =1 × 12 × 2

=14

 

Example2: Solve 78÷14.

Solution: 

 78÷14

Change division to multiplication by applying the "Keep, Change, & Flip" rule.

= 78 × 41

Multiply across the numerators and denominators.

=7 × 48 × 1

=288         (simplify the fraction by reducing it to its lowest terms.)

=28 ÷ 48 ÷ 4

=72

Convert the improper fraction to the mixed number by dividing the numerator by the denominator.

=312

 

Cheat Sheet

  • Any whole number can be written as a fraction, such as 5 can be written as  51
  • While creating an equivalent fraction, both the numerator and the denominator of the fraction must be multiplied/divided by the same number. 
  • Always simplify the fraction whenever needed and possible. Sometimes a fraction can be simplified before multiplying/dividing. 
  • A fraction multiplied by its reciprocal equals 1.

                                                           12·21=1

  • The division is the inverse operation of multiplication; every division expression can be written as a multiplication expression by following the division rule of "keep, change, & flip."

                                                          1 ÷ 7 = 1 × 17

  • The reciprocal of 3 is 13 . The multiplication inverse of 3 is 13.

Blunder Areas

  • The word "of" means multiplication.

For example, Mr. Jim's house is 34miles from the school. He walks 23of the distance and then jogs the rest. How many miles does he walk?

        Solution: In this scenario, it's 23of 34miles. Therefore, 23×34612 = 12

  • While multiplying two fractions, the numerator should be multiplied with the numerator and the denominator with the denominator.
  • Always reduce the answer to its lowest term.