Math 6 Honors (Period 6 and 7)

Multiplication and Division of Mixed Numbers 7-5

One method of finding the product of two mixed numbers is to first change the mixed numbers into improper fractions and then multiply

6 X 3 1/12 becomes
6/1 X 37/12
Simplify using the methods taught and reviewed this week
6/1 X 37/ 12 = 37/6 = 18 1/2

5 3/4 X 4 2/3
23/4 X 14/3 becomes
23/2 X 7/ 3 = 161/6 = 26 5/6

13 1/3 X 15 3/4
40/3∙ 63/4
simplify ( GCF of 40 and 4 is 4 and GCF of 3 and 63 is 3) to
10/1 ∙ 21/1 = 210



To divide one mixed number by another, we change the mixed numbers into improper fractions and use the methods from the previous lessons

2 2/3 ÷ 10 2/3 first change to improper fractions
8/3 ÷ 32/3 Remember. that dividing by a fraction is the same a multiplying by its reciprocal
8/3 X 3/32
Using the GCF to simplify first
1/1 X 1/4 = 1/4

What about
1 7/15 ÷ 5 1/2
22/15 ÷ 11/2
22/15 X 2/11 = 4/15

or 42 2/3 ÷ 3 5/9

128/3 ÷ 32/9
128/3 ∙ 9/32
simplify and you get
4/1 ∙ 3/1 = 12

hat if we have equations such as the book shows
n X 2 1/3 = 6 5/12
First rewrite it as (2 1/3)n = 6 5/12
Then change the mixed numbers to improper fractions
(7/3)n = 77/12
Now, we know to isolate the variable, we must use the inverse operation and in this case we would multiply 7/3 by its reciprocal 3/7 to both sides
(3/7)(7/3) n = (77/12)(3/7)
n = 11/4
n = 2 3/4