This document provides instructions for performing operations on fractions, including: 1. To multiply fractions, multiply the numerators and denominators. 2. To divide fractions, invert the second fraction and multiply. 3. To add fractions, find a common denominator that is a factor of both denominators so the fractions can be added.

1. +
Fractions
Multiplication
and Division

2. +Multiplication
Multiply the numerators and put in
the numerator of the result
Multiply the denominators and put
in the denominator of the result
8 9 8 x 9 72
47 7 x 4 28
= =x

3. +Multiplication - Let’s Try It!
9 2
17
=x
5 3
17
=x
7 11
94
=x
4 14
730
=x
18
7
15
7
77
36
56
210

4. +
56
210 These numbers get
pretty big!
What if we needed
to multiply again?
Let’s make the fraction more simple,
so it will be easier to use in the future.

5. +Simplification
 Divide by the Greatest Common Factor
72
28
But what is a
Common Factor?

6. +
Factors
A factor is a number that can be divided
into another number with no remainder
 8’s factors are:
 1 (8/1 =8)
 2 (8/2 = 4)
 4 (8/4 = 2)
 8 (8/8 = 1)
 3 is NOT a factor of 8, because 8 is not evenly divisible by 3 (8/3 = 2
with R=3)

7. +
Common Factors
A common factor is a factor that
two numbers have in common
 For example, 7 is a factor of both 21 and 105,
so it is a common factor of the two.
 The greatest common factor is the largest
factor that the two number share
So let’s go back to our simplification
problem from before…

8. +
Simplification
Divide both numerator and denominator by
the Greatest Common Factor
72
28 Factors are 1, 2, 4, 7, 14, 28
Factors are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 48, 72
Greatest Common Factor is 4
28
72 ÷
÷ 4
4
=
=
7
18
So
72
28
=
7
18

9. +
Simplification - Let’s Try It!
3
1
7
2
3
1
63
18
=
5
2
114
78
=
7
2
19
13
9
3
=
84
24
=
21
7
=
15
6
=

10. +Division
Just like multiplication with one more step
Invert the second fraction and multiply
8 2
13
=÷
8 1
23
x =
8
6

11. +
Division - Let’s Try It!
9 2
17
=÷
=
5 3
17
÷
7 11
94
=÷
=
4 10
720
÷
9
14
5
21
63
44
7
50

12. +Addition
To add two fractions, you must make
sure they have a Common Denominator
8
3
16
5
+
What is a
Common
Denominator?

13. +
Common Denominator
 A common denominator is a number with which
both of the denominators share at least one factor
that is not the number 1
 For example, if the denominators are 4 and 7, then a
common denominator is 28.
 28 shares the factors 1, 2 and 4 with the number 4,
and the factors 1 and 7 with the number 7.
So let’s go back to our simplification
problem from before…

14. +
Review
 A fraction has a numerator and a denominator
 The denominator can never be 0
 You can multiply, divide, add and subtract fractions
 A common factor is a number that both
denominators are evenly divisible by
 A common denominator is a number that both