Bell Work!!!

1. a ÷ (b)

2. c × d

3. d ÷ d

4. c × b

- 2

12

1

-15

a= -10 b= 5 c= - 3 d= - 4

Rational NumbersRational 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.

4 4

1

Multiplying FractionsMultiplying Fractions

• 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:

2

5

9

2

2 9

5 2

18

10

3

4

5

2

35

4 2

15

8

2

2

9

5

= 1

= 1

Cross CancelingCross Canceling

• 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:

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 cross cancel, it is just an option. If you are more comfortable, multiply across and simplify at the end.

= 1

= 1

Mixed NumbersMixed Numbers

• To multiply mixed numbers, convert them to improper fractions first.

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= 4

Sign RulesSign Rules

• Remember, when multiplying signed numbers...

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

Try These: MultiplyTry These: Multiply

Multiply the following fractions and mixed numbers:

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

= 6

= 6

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

= 6

Dividing FractionsDividing Fractions

• When dividing fractions, they do NOT need to have a common denominator.

• To divide two fractions, change the operation to multiply and take the reciprocal of the second fraction (flip the second fraction). Keep-Change-Change.

2

5

9

2

2

5

2

9

Change Operation.

Flip 2nd Fraction.

Dividing FractionsDividing Fractions

• Finish the problem by following the rules for multiplying fractions.

2

5

9

2

2

52

9

4

45

Try These: DivideTry These: Divide

• Divide the following fractions & mixed numbers:

1) 6

5

1

2

2)

3

2

1

2

3) 21

33

2

34)

7

31

2

3

Solutions: DivideSolutions: Divide

1) 6

5

1

2

6

5

2

1

12

5

2) 3

2

1

2

3

2

2

1

6

2

2

2

3

13

3) 21

33

2

3

7

3

11

3

7

3

3

11

21

33

3

3

7

11

4) 7

31

2

3

7

3

5

3

7

33

5

21

15

3

3

7

5

= - 2

= - 1

Converting Fractions to Decimals

To convert a fraction to a decimal, divide the numerator by the denominator.

*remember :

You will get a decimal that terminates or repeats.

*terminates: 0.125 *repeats: 0.666If it repeats, place a bar (--- ) over the first

number that repeats.

= 2 ÷ 5 = 5 2

18

180

.0.1

-82

002

-164

005

Top In Bottom Out

-4 0

45

450

.0.8

-400

Top In Bottom Out

28

280

.0.2

-164

005

-40

Top In Bottom Out

23

230

.0.6

-182

00

Top In Bottom Out

6

35

350

.0.6

-300

Top In Bottom Out