Fraction Basics

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Fraction Basics

• Richard Dunton
• University of Phoenix Online
• EDTC 560
• Janet Wright
• August 25, 2004

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We will learn to

• Identify and write proper fractions
• Identify and write improper fractions and mixed
  numbers
• Create equivalent fractions
• Reduce fractions to lowest terms
• Raise fractions to higher terms

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What is a proper fraction?

• A proper fraction stands for part of a whole or
  of a group
• The smaller number, the part, is on top and the
  larger number, the whole, is on the bottom
• The top number is called the numerator
• The bottom number is called the denominator

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The whole maybe a single object

• Count the number of equal parts in the circle.
  This number is the denominator and is equal to 4.
• Count the number of shaded parts. This is the
  numerator and is equal to 3
• What fractional part of the circle is shaded?

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Thats right

• 3 parts of the circle are shaded
• The circle is divided into 4 equal parts
• Read 3/4 as three-fourths
• Numerator ? 3/4 ? denominator

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Or it maybe a group of objects

• What fraction of the group of circles is shaded?

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• Four out of five circles are shaded
• Numerator ? 4/5 ? denominator
• Read as four-fifths

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Writing improper fractions and mixed numbers

• In an improper fraction the numerator is equal to
  or larger than the denominator
• A mixed number has a whole number and a fraction
  part
• You may need to change an improper fraction to a
  whole or mixed number

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Writing improper fractions

• The top number (numerator) stands for the number
  of shaded pieces
• The bottom number (denominator) stands for number
  of pieces in 1 wholein this case four
• Therefore here we have 4/4 or 1 whole pizza pie

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Writing improper fractions

• In an improper fraction there are more pieces
  then are defined by 1 whole
• Here each pie is divided into 5 equal parts
• What fraction do these two pies represent?

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Writing improper fractions

• In the last example we have 9 parts
• The 2 pies divided into 5 equal portions
• There are 4 pieces more than 1 whole
• Therefore, we write it as 9/5, read as nine-tenths

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Writing mixed numbers

• A mixed number is a whole number together with a
  fraction
• You can rewrite an improper fraction as a mixed
  number by dividing the denominator into the
  numerator and writing the remainder over the
  denominator
• Notice that 9/5 and 1 4/5 represents the same
  amount

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Changing a mixed number to an improper fraction

• Using 1 4/5 as an example
• Multiply the whole number by the denominator
• Add the numerator to it, and
• Put the total over the denominator
• 5 x 1 4 / 5 9/5

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Equivalent fractions

• Each of the circles represents 1 whole pizza pie
• In the first pie 1 of 2 equal parts is shaded in
  the second 4 of 8 are shaded
• Both represent 1/2 of a pizza pie, as the same
  area is shaded in each circle
• Equivalent fractions are different fractions that
  represent the same amount

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Renaming fractions to lowest terms

• Fractions are reduced to lowest terms by dividing
  both the numerator and denominator by the same
  number
• A fraction is in lowest terms when 1 is the only
  number that can divide evenly into both the
  numerator and the denominator

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Reduce fractions to lowest terms

• In the equivalent fraction example 1/2 is the
  same as 2/4
• We reduce the second fraction (2/4) by diving the
  numerator and denominator by 2
• Therefore 2/4 2 2/ 4 2 1/2

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Raising fractions to higher terms

• When you change a fraction to an equivalent
  fraction with a higher denominator, you raise it
  to higher terms
• To raise a fraction to higher terms, multiply
  both the numerator and denominator by the same
  number

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Examples

• Multiply the numerator and denominator by 2 to
  raise each fraction to higher terms
• 2/3 2 x 2 / 2 x 3 4/6
• 3/5 3 x 2 / 2 x 5 6/10
• 4/7 4 x 2 / 7 x 2 8/14

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We have learned to

• Identify proper fractions
• Write improper fractions and mixed numbers
• Create equivalent fractions
• Reduce fractions to lowest terms
• Raise fractions to higher terms

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Congratulations!!!

• We are now ready to learn how to add subtract,
  multiply an divide fractions