Multiplying Rational Multiplying Rational NumbersNumbers

(Multiplying Fractions)(Multiplying Fractions)

DART statement:

I can multiply fractions (rational numbers).

• 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

• Convert to improper fractions.

• Simplify.

• Multiply straight across.

Mixed NumbersMixed Numbers

• Try these on your own.

Mixed NumbersMixed Numbers

• 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

Solutions (alternative): MultiplySolutions (alternative): Multiply

1) 6

5

1

3

2) 51

36

5

16

36

5

4) 4

96

8

Note: Problems 1, 2 and 4 could have been simplified before multiplying.

2

5

32

5

1

2

2

1

1

96

2

1

2

1

93

11

3

1

3

1

3