Unit 4 : Multiply and Divide Fractions
Friendly Notes
Product of Fractions
When multiplying a fraction by another fraction, we multiply
the numerators and the denominators separately.
1. Multiply
2
7
by .
3
10
Method 1:
1
2
7
2×7
×
=
3 10
3 × 105
7
=
15
Method 2:
2
7
7
×
=
3 105
15
1
2.
3
1
of a class are girls. of the girls have long hair. What
4
6
fraction of the class are girls with long hair?
1
3
3
× =
6 4 24
1
=
8
1
of the class are girls with long hair.
8
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Word Problems
A book has 250 pages. Melissa read
and
1
of the book on Friday
5
1
of the remaining pages on Saturday. How many pages
8
did she read on Saturday?
250
?
Method 1:
1−
1
4
=
5 5
She had
4
of the pages in the book left to read on Friday.
5
1
2
1
4
1
× =
8 5 10
She read
1
of the pages in the book on Saturday.
10
1
× 250 = 25
10
Melissa read 25 pages on Saturday.
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250
Method 2:
1−
1
4
=
5 5
?
4
She had of the pages in the book left to read on Friday.
5
50
4
× 250 = 200
5
1
She had 200 pages left on Friday.
25
1
× 200 = 25
8
1
Melissa read 25 pages on Saturday.
Dividing a Fraction by a Whole Number
1. Divide
2
by 4.
3
2
Divide 3 into 4 equal parts.
2
3
1
2
3
2
Each part is 4 of 3 .
2
2
1
÷ 4= ×
3
3 4
2
=
12
1
=
6
1
4
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3
2. 3 children shared of a pie equally. How much pie did each
5
of them get?
3
3
1
÷3= ×
5
5 3
3
=
15
1
=
5
Each of them got
Dividing by 3 is the same
1
as multiplying by 3 .
1
of the pie.
5
Dividing by a Fraction
1. Rita bought 4 pies. She cut each pie into fifths. How many
pieces of pie did she have?
There are 5 fifths
in 1 whole.
There are 20
fifths in 4 wholes.
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1
1
5
Dividing by 5 is the same
4 ÷ = 4 × 5
as multiplying by 5.
= 20
1
5 is the reciprocal of 5 .
Rita had 20 pieces of pie.
2
5
2. Divide 5 by .
5
2
5
2
5
2
5
2
5
2
5
5÷ =5×
5
2
25
=
2
1
= 12 2
2
5
2
5
2
5
2
5
2
5
2
5
2
5
2
5
Dividing by 2
is the same
5
5
as multiplying by 2 .
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3. Divide
1
1
by .
4
8
1
Divide 4 into eighths.
1
There are 2 eighths in 4 .
1
4
1
8 is the reciprocal of 8 .
1
8
1
1
1
÷ = × 8
4 8 4
8
=
4
1
Dividing by 8 is the
same as multiplying by 8.
= 2
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