(The easiest operations)
Multiplication: When multiplying fractions, simply multiply numerator
times numerator, and denominator times denominator.
Example:
1
5
1 times 2 is 2
x 2
3
=
2
15
5 times 3 is 15
Sometimes you will have to reduce.
Example:
3
4
x
2
3
=
6
12
6 goes into 6 one time
1
6
12 2
Reduce
1
2
=
6 goes into 12 two times
In the above example, you could have cross-canceled.
This is another method of reducing.
Example:
2 goes into itself
one time
3 goes into itself
one time
3
4
1
x
Now reduce
the 2 and the 4
2
3
1
3 goes into
3 one time
The Academic Support Center at Daytona State College (Math 4 pg 1 of 2)
1
1
3
4
x
2
1 times 1 is 1
2
3
=
1
2
1
2 goes into 4
two times
2 times 1 is 2
Division: When dividing a fraction by a fraction, invert the second fraction, and
then follow the rules for multiplication.
Example:
1
3
÷
5
4
Invert the 1/5
then multiply
3 x 5
1
4
=
15
4
Notice we ended up with an improper fraction, 15/4. You can change it into a mixed
fraction if you wish; however, in algebra, improper fractions are easier to work with.
The next example involves the same division problem in the form of a complex fraction
(a fraction within a fraction). Invert the fraction in the denominator, and then multiply.
Example:
3
4
1
5
Invert the 1/5
then multiply
x 5
1
3
4
15
4
=
Notice when we inverted 1/5, it became 5/1, which is the same as 5 (a whole number).
When multiplying fractions by whole numbers, place the whole number over 1 so that
you can multiply numerator times numerator and denominator times denominator.
Example:
2
7
x 2
Place 2 over 1
2
7
x 2
1
=
4
7
Practice Problems:
a) 1 x 3
10
b) 5 x 3
4
6
c)
2
5
2
5
 Answers to Practice Problems:
The Academic Support Center at Daytona State College (Math 4 pg 2 of 2)
3
8
d) 2 x 3
a) 3/10
b) 5/8
e)
c) 1
7
1
÷ 3
9
d) 4
e) 7/3
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Multiplication: