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### Mixed Numbersand Rational Numbers

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

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 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

- 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

- 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

- 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

=

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.

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

Multiply the following fractions and mixed numbers:

Reciprocal

- The reciprocal is the “multiplicative inverse”
- This means to flip the fraction over, so…

2

3

3

2

The reciprocal of is

!

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 Fractions

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

Try These: Divide

- Divide the following fractions & mixed numbers:

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

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