Multiplying Rational Multiplying Rational NumbersNumbers
(Multiplying Fractions)(Multiplying Fractions)
• The term Rational Numbers refers to any number that can be written as a fraction.
• This includes fractions that are reduced, fractions that can be reduced, mixed numbers, improper fractions, and even integers and whole numbers.
• An integer, like 4, can be written as a fraction by putting the number 1 under it.
Rational NumbersRational Numbers
4 4
1
• When multiplying fractions, they do NOT need to have a common denominator.
• To multiply two (or more) fractions, multiply across, numerator by numerator and denominator by denominator.
• If the answer can be simplified, then simplify it.
• Example:
• Example:
Multiplying FractionsMultiplying Fractions
2
5
9
2
2 9
5 2
18
10
3
4
5
2
35
4 2
15
8
2
2
9
5
• When multiplying fractions, we can simplify the fractions and also simplify diagonally. This isn’t necessary, but it can make the numbers smaller and keep you from simplifying at the end.
• From the last slide:
• An alternative:
Simplifying DiagonallySimplifying Diagonally
2
59
2
2 9
5 2
18
10
2
2
9
5
2
59
2
1
1
19
5 1
9
5
You do not have to simplify diagonally, it is just an option. If you are more comfortable, multiply across and simplify at the end.
• To multiply mixed numbers, convert them to improper fractions first.
Mixed NumbersMixed Numbers
32
5
1
1
4
35 2
5
14 1
4
17
5
5
4
17
5
5
4
1
1
17 114
17
4
• Remember, when multiplying signed numbers...
Sign RulesSign Rules
1) 3
8
2
5
Positive * Positive =
Negative * Negative =
Positive * Negative =
Positive.
Positive.
Negative.
6
40
2
2
3
20
2) 3
10
1
6
3
60
3
3
1
20
Multiply the following fractions and mixed numbers:
Try These: MultiplyTry These: Multiply
1) 6
5
1
3
2) 5
1
36
5
3) 13
4
3
1
2
4)
4
96
8
Solutions: MultiplySolutions: Multiply
1) 6
5
1
3
6
15
3
3
2
5
2) 51
36
5
16
3
6
5
96
15
3
3
32
5
3) 13
4
3
1
2
7
4
7
2
49
8
4) 4
96
8
24
72
24
24
1
3