Bell Ringer

Two boys decided to share a pizza. Johnny ate ½ of the original pizza. Jimmy ate ½ of what was left. How much of the pizza remains? (Hint: Draw a picture.)

Johnny

Jimmy

¼ Remains

Mixed Numbersand Rational Numbers

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.

3

414 =

Rational Numbers

Types of Rational Numbers

• Reduced Fractions:

• Not Reduced Fractions:

• Mixed Numbers:

• Improper Fractions:

• Integers and Whole Numbers: -5, 12, 5

4

23

15 8

132

68

Improper Fractions

To convert an improper fraction to a mixed number:

Divide the denominator into the numerator. Put the remainder over the denominator.

3=15 4

34

Mixed Numbers

Converting Improper Fractions to Mixed Numbers:

Multiply the denominator by the whole number.

Add the numerator.

445

= 24 5 31

722 7

=

Multiplying and Dividing 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.

Multiplying Fractions

2

5

9

2

2 9

5 2

18

10

3

4

5

2

35

4 2

15

8

2

2

9

5= 4

51

=178

• 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 Diagonally

2

5

9

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.

45

=1

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

Mixed Numbers

32

5

1

1

4

35 2

5

14 1

4

17

5

5

4

17

5

5

4

1

1

17114

17

4144=

• Remember, when multiplying integers...

Integer Rules

1) 3

8

2

5

Positive * Positive =

Negative * Negative =

Positive * Negative =

Positive.

Positive.

Negative.

2) 3

10

1

6

320

= _

= 120

1

1

4

2

Multiply the following fractions and mixed numbers:

Try These: Multiply

1) 6

5

1

3

2) 5

1

3

6

5

3) 13

4

3

1

2

4)

4

96

8

Reciprocal

The reciprocal is the “multiplicative inverse”

This means to flip the fraction over, so…

23

The reciprocal of is

32

!

What is my reciprocal?

15

124

49

78

23

10 3

452 3 -1

• 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.

Dividing Fractions

2

5

9

2

2

52

9

Change Operation.

Flip 2nd Fraction.

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

Dividing Fractions

2

5

9

2

2

5

2

9

4

45

• Divide the following fractions & mixed numbers:

Try These: Divide

1) 6

5

1

2

2)

3

2

1

2

3) 21

33

2

34)

7

31

2

3

More than Two Fractions!!!

You can cancel any number from the top with any number from the bottom as long as they have a common factor.

38

5 9

45

• • =1 1

1

1

2 3

1 6

Try This One!!!!!

57

23 -47

8 3 10

12

• ••• =_