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Multiplying and Dividing 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.

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. - Example
- Example

Simplifying Diagonally

- When multiplying fractions, we can simplify the

fractions and also simplify diagonally. This

isnt necessary, but it can make the numbers

smaller and keep you from simplifying at the end. - From the last slide
- An alternative

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 Numbers

- To multiply mixed numbers, convert them to

improper fractions first.

Sign Rules

- Remember, when multiplying signed numbers...

Positive Positive

Positive.

Negative Negative

Positive.

Positive Negative

Negative.

Try These Multiply

- Multiply the following fractions and mixed

numbers

Solutions Multiply

Solutions (alternative) Multiply

Note Problems 1, 2 and 4 could have been

simplified before multiplying.

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

Solutions Divide

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