Multiplying & Dividing Mixed Numbers

 

To multiply or divide mixed numbers, first convert each mixed number to an improper fraction.

 

Multiply

 

  • First, multiply the two numerators of the fractions.
  • Then, multiply the two denominators of the fractions.
  • Then, simplify the resulting fraction.
  • Finally, convert the improper fraction from the previous step to a mixed number.

 

Example:

 

4 3/5 X 2 7/8 = ?

 

  • Convert both mixed numbers to improper fractions:

 

4 3/5 = 23/5

2 7/8 = 23/8

 

23/5 X 23/8 = ?

 

  • Multiply the numerators ( 23 X 23 = 529)
  • Next, multiply the denominators( 5 X 8 = 40)

 

23/5 X 23/8 = 529/40

 

  • Convert to a mixed number

 

529/40 = 13 9/40

 

Divide

 

  • First, invert the divisor (the second fraction) – this means turn the fraction upside down. 23/8 becomes 8/23.
  • Then, multiply the two fractions following the steps from above.

 

Example:

 

4 3/5 ÷ 2 7/8 = ?

 

  • Convert both mixed numbers to improper fractions:

 

4 3/5 = 23/5

2 7/8 = 23/8

 

23/5  ÷  23/8 = ?

 

  • Invert the divisor ( 23/8 becomes 8/23)

 

Now multiply the two fractions:

 

23/5 X 8/23

 

  • Multiply the numerators ( 23 X 8 = 184)
  • Next, multiply the denominators( 5 X 23= 115)

 

23/5 X 8/23 = 184/115 (This fraction is already simplified.)

 

  • Convert to a mixed number

 

184/115 = 1 69/115