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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.). Jimmy. Johnny. ¼ Remains. Mixed Numbers and Rational Numbers. Rational Numbers.

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Bell ringer
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.)

Jimmy

Johnny

¼ Remains


Mixed numbers and rational numbers

Mixed Numbersand Rational Numbers


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.

4

4 =

1


Rational numbers1
Rational Numbers

Types of Rational Numbers

  • Reduced Fractions:

  • Not Reduced Fractions:

  • Mixed Numbers:

  • Improper Fractions:

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

2

3

6

8

1

3

2

15

8


Improper fractions
Improper Fractions

  • To convert an improper fraction to a mixed number:

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

15

4

3

3

4

=


Mixed numbers
Mixed Numbers

  • Converting Improper Fractions to Mixed Numbers:

  • Multiply the denominator by the whole number.

  • Add the numerator.

4

4

5

24

5

3

22

7

1

7

=

=



Multiplying fractions
Multiplying 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.

4

5

1

=

7

8

1

=


Simplifying diagonally

1

1

Simplifying Diagonally

  • 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:

4

5

1

=

You do not have to simplify diagonally, it is just an option. If you are more comfortable, multiply across and simplify at the end.


Mixed numbers1

1

1

Mixed Numbers

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

1

4

4

=


Integer rules
Integer Rules

  • Remember, when multiplying integers...

Positive * Positive =

Positive.

Negative * Negative =

Positive.

Positive * Negative =

Negative.

1

_

3

20

=

4

1

1

20

=

2


Try these multiply
Try These: Multiply

Multiply the following fractions and mixed numbers:


Reciprocal
Reciprocal

  • The reciprocal is the “multiplicative inverse”

  • This means to flip the fraction over, so…

2

3

3

2

The reciprocal of is

!


What is my reciprocal
What is my reciprocal?

1

5

10

3

7

8

4

9

1

2

2

3

4

5

2

3

-1

4


Dividing fractions

Change Operation.

Flip 2nd Fraction.

Dividing 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.


Dividing fractions1
Dividing Fractions

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


Try these divide
Try These: Divide

  • Divide the following fractions & mixed numbers:


More than two fractions
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.

1

1

1

3

8

4

5

5

9

1

6

=

1

2

3


Try this one
Try This One!!!!!

5

7

2

3

3

10

7

8

-4

1

2

_

=


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