# NOTES:Multiplying and Dividing Fractions/Mixed Num - Multiplying and Dividing Fractions/Mixed Number

•  Multiplying and Dividing Fractions/Mixed Numbers

Multiplying fractions:

First, Multiply the numerators to get the new numerator.

Second, Multiply the denominators to get the new denominator.

Lastly, Reduce or Simplify the fraction by dividing numerator and denominator by the GCF(largest number that goes into both the numerator and denominator.)  If the fraction is improper, change to a mixed or whole number

¾  x 2/3 = 3 x 2 = 6_   numerator (dividend)

4 x 3 = 12   denominator (divisor)

6/12 can be reduced or simplified because, 6 is the GCF(greatest common factor of 6 and 12), divide numerator and denominator by the GCF of 6:

6    ÷ 6 (GCF) = 1

12  ÷ 6(GCF)  = 2          so  6/12  =  ½

NOTE:  you can reduce before you multiply the numerator and the denominator as long as you simplify any numerator with any denominator

In ¾ x 2/3  the numerator 3 of 3/4 and the denominator 3 of 2/3 can both be divided by 3 so you would have

¼ x 2/1.  Now the denominator 4 of ¼ and the numerator 2 of 2/1 can be simplified by 2 so divided 2 by 2 and get 1, then divide 4 by 2 and have 2.

½ x 1/1 = 1/2

Multiplying with a Whole Number:   turn a whole number into a fraction by placing a 1 under it   6 = 6/1

Multiplying Mixed Numbers:

In order to multiply 2 1/3 x 1 3/5

First, change each mixed number into an improper fraction by taking the denominator x whole number then adding the numerator to get the new numerator, denominator stays the same.

2        1/3 = 3(denominator) x 2(whole number) = 6 + 1(numerator) = 7  so 7/3

1  3/5  = 5(denominator) x 1(whole number)= 5 + 3(numerator) = 8  so 8/5

Second, multiply   7/3 x 8/5  =  Numerators     7 x 8 =  56

Denominators 3 x 5 =  15

Improper to mixed:  56/15 is improper so change into a mixed number  56 divided by 15 (how many times does 15 go into 56?

15 goes into 56:  3 whole times(3 x 15 = 45)

56 – 45 = remainder of 11

DENOMINATOR STAYS THE SAME when  changing improper to mixed or mixed to improper

So  56/15 = 3  11/15  since 11 and 15 only have 1 as a common factor,  it cannot be reduced or simplified.

Dividing Fractions:

When you divide fractions, you multiply the first fraction by the reciprocal of the 2nd fraction.

Reciprocal is the “flip” of a fraction -- reciprocal of 3/7  is 7/3 (The product of  a fraction and its reciprocal = 1)

First,   3/8 ÷ 3/7   =  3/8(first fraction) x  7/3(reciprocal of 2nd fraction)    =   3/8 x 7/3

Second,  multiply numerators and denominators and reduce/simplify if you can

Numerators        3 x 7  =  21

Denominators    8 x 3  =  24     the GCF of 21 and 24 is 3 so divide numerator and denominator by 3

GCF

21 ÷ 3     =  7

24 ÷ 3     =  8        so 3/8 ÷ 3/7 =  7/8

Dividing Mixed Numbers:

When dividing mixed numbers:        4 ½ ÷  2 ¾

First, change the mixed numbers into improper fractions  4 ½ = 9/2    and 2  ¾ = 11/4

Second, multiply the first fraction by the reciprocal (flip) of the second fraction as above.