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 isn’t necessary, but it can make the numbers smaller and keep you from simplifying at the end.
• From the last slide:

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• 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 =

Negative * Negative =

Positive * Negative =

Positive.

Positive.

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