Multiplying Rational Numbers

1. Multiplying RationalMultiplying Rational
NumbersNumbers

2. • 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

3. • 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
=
3⋅ 5
4 ⋅2
=
15
8
÷2
÷2
=
9
5

4. • 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
5
⋅
9
2
=
2 ⋅ 9
5 ⋅ 2
=
18
10
÷2
÷2
=
9
5
2
5
⋅
9
2
1
1
=
1⋅ 9
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.

5. • To multiply mixed numbers, convert them to
improper fractions first.
Mixed NumbersMixed Numbers
3
2
5




1
1
4




=
3⋅5 + 2
5




1⋅ 4 +1
4




=
17
5




5
4




=
17
5




5
4




1
1
=
17 ⋅1
1⋅ 4
=
17
4

6. • 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

7. Multiply the following fractions and mixed numbers:
Try These: MultiplyTry These: Multiply
1)
6
5
−
1
3



 2) 5
1
3
⋅
6
5
3) −1
3
4




−3
1
2



 4)
4
9
⋅
6
8

8. Solutions: MultiplySolutions: Multiply
1)
6
5
−
1
3



 = −
6
15
÷3
÷3
= −
2
5
2) 5
1
3
⋅
6
5
=
16
3
⋅
6
5
=
96
15
÷3
÷3
=
32
5
3) −1
3
4




−3
1
2




= −
7
4




−
7
2




=
49
8
4)
4
9
⋅
6
8
=
24
72
÷24
÷24
=
1
3

9. Solutions (alternative): MultiplySolutions (alternative): Multiply
1)
6
5
−
1
3




2) 5
1
3
⋅
6
5
=
16
3
⋅
6
5
4)
4
9
⋅
6
8
Note: Problems 1, 2 and 4 could have been simplified before
multiplying.
= −
2
5
=
32
5
1
2
2
1
=
1
9
⋅
6
2
1
2
=
1
9
⋅
3
11
3
=
1
3
1
3

10. Solutions (alternative): MultiplySolutions (alternative): Multiply
1)
6
5
−
1
3




2) 5
1
3
⋅
6
5
=
16
3
⋅
6
5
4)
4
9
⋅
6
8
Note: Problems 1, 2 and 4 could have been simplified before
multiplying.
= −
2
5
=
32
5
1
2
2
1
=
1
9
⋅
6
2
1
2
=
1
9
⋅
3
11
3
=
1
3
1
3