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Fraction Basics
Richard Dunton
University of Phoenix Online
EDTC 560
Janet Wright
August 25, 2004
We will learn to…
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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
What is a proper fraction?
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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
The whole maybe a single
object…
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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?
That’s right…
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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
Or it maybe a group of objects…
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What fraction of the
group of circles is
shaded?
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Four out of five circles are shaded
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Numerator → 4/5 ← denominator
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Read as four-fifths
Writing improper fractions and
mixed numbers
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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
Writing improper fractions
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The top number (numerator)
stands for the number of shaded
pieces
The bottom number
(denominator) stands for
number of pieces in 1 whole…in
this case four
Therefore here we have 4/4 or 1
whole pizza pie
Writing improper fractions
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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?
Writing improper fractions
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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 ninetenths
Writing mixed numbers
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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
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
Equivalent fractions
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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
Renaming fractions to lowest
terms
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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
Reduce fractions to lowest
terms
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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
Raising fractions to higher
terms
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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
Examples
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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
We have learned to…
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Identify proper fractions
Write improper fractions and mixed
numbers
Create equivalent fractions
Reduce fractions to lowest terms
Raise fractions to higher terms
Congratulations!!!
We are now ready to learn
how to add subtract,
multiply an divide fractions