Multiplying and Dividing Rational Numbers

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Multiplying and Dividing Rational Numbers
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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.

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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

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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.
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Mixed Numbers

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

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Sign Rules

• Remember, when multiplying signed numbers...

Positive Positive
Positive.
Negative Negative
Positive.
Positive Negative
Negative.
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Try These Multiply

• Multiply the following fractions and mixed
  numbers

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Solutions Multiply
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Solutions (alternative) Multiply
Note Problems 1, 2 and 4 could have been
simplified before multiplying.
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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.

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Dividing Fractions

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

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Try These Divide

• Divide the following fractions mixed numbers

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Solutions Divide