Multiplying and Dividing Rational Numbers

1
Multiplying and Dividing Rational Numbers
2
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

3
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.
4
Mixed Numbers

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

5
Sign Rules

• Remember, when multiplying signed numbers...

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Try These Multiply

• Multiply the following fractions and mixed
  numbers

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Solutions Multiply
8
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.
• The rules for signs are the same as
  multiplication
• To divide two fractions, change the operation to
  multiply and take the reciprocal of the second
  fraction (flip the second fraction).
  Keep-Switch-Flip.

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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