Multiplying, Simplifying, and Dividing Fractions

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Multiplying, Simplifying, and Dividing Fractions

• 3-1

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Whole Numbers

• Whole units, such as 1 or 6000

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Fractional Numbers

• The number that results when one number is
  divided by another and the quotient is not a
  whole number

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Fractional Numeral

• A symbol for a fractional number

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Terms

• The numerator and denominator of a fraction

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Numerator

• The numeral above the line in a fraction,
  indicating how many of the equal parts of the
  fraction are shown

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Denominator

• The numeral below the line in a fraction, showing
  the of equal parts into which a whole is
  dividing

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Multiplying Fractions

• Multiply straight across
• Example
• of x

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Equivalent Fractions

• Fractions that name the same (i.e., they are
  equal)
• As long as you do the same thing to both the top
  and bottom of a fraction, the beginning and
  ending fractions will be equivalent
• Example
• x 2
• x 2

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Visualize...
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Simplest/Lowest Terms

• Occurs when no number other than 1 will divide
  into both terms of a fraction
• Example
• 2
• 2

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Simplifying Using Cancellation

• As long as one is on the top and the other is
  on the bottom, you can divide out common factors,
  then multiply across
• Example
• x

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Proper Fraction

• A fraction in which the numerator is smaller than
  the denominator

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Improper Fraction

• A fraction whose numerator is equal to or greater
  than the denominator

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Mixed Number

• A number having both a whole number and a fraction

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Mixed to Improper

• Multiply the whole number times the denominator,
  then add the numerator and put that over the
  original denominator
• Example

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Improper to Mixed

• See how many times the denominator goes into the
  numerator (this is your whole )
• Multiply the whole times the denominator, then
  subtract from the numerator to see what is left
  over (that is the new numerator)
• Put that over the same denominator

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Example
or
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Reciprocal

• The number whose product with the given is 1
  (or, flipping the fraction)
• Example
• or

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Dividing Fractions

• Change to multiplication and use the reciprocal
  of the 2nd fraction (flip it)
• Example
• x

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Multiplying/Dividing a Decimal and a Fraction

• When multiplying a whole by a fraction, just
  multiply the whole by the numerator and divide
• Example
• x

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Homework

• Pages 81-85
• 3, 4, 6, 13, 15, 18, 29, 35, 45, 49, 55, 65, 69