Equivalent Fractions

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Equivalent Fractions
Fractions are equivalent (equal) if they have the
same value
We could change them to decimals to see if they
are equal or leave them as fractions
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We know that we can multiply or divide by 1 and
the number stays the same
Since
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We can multiply or divide any fraction by these
and the fraction keeps its value
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?



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What if we have 2 fractions like
Why might we want them to have the same
denominator?
to compare
to add or subtract
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We need to find a common denominator
? 5
? 8
? 8
? 5
6
There are many common denominators, but only one
is the smallest
? 6
? 8
? 8
? 6
Is there a smaller denominator we could use?
Yes, 24!
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What we are doing is looking at the multiples of
numbers
The multiples of 6 are
6, 12, 18, 24, 30, 36, 42, 48 and so on
The multiples of 8 are
8, 16, 24, 32, 40, 48 and so on
Both 24 and 48 are common, but 24 is the least
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Remember! You CANT have a Greatest Common
Multiple! Why not?
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Lets compare some fractions
Which is larger,
What is the LCD?
Yes, 24
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Compare these
The multiples of 16 are 16, 32, 48, 64, 80
The multiples of 12 are 12, 24, 36, 48, 60
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Lets practice on whiteboards!
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Another way of using equivalent fractions is to
put fractions in simplest form or lowest terms
Would this fraction be easier to understand if
the numbers were smaller?
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We know we can divide both the numerator and
denominator by the same number and get an
equivalent fraction
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2
6
Sure, there are many, but lets try 6


2
6
Now 2
What number goes into both 36 and 96?
15
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We could have done this in one step if we had
used the GCF of 36 and 96

12
12
The GCF of 36 and 96 is
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Practice
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We can also multiply the numerator and
denominator by the same number
? 2

? 2
Why would we want to do that?
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? 2
? 3


? 2
? 3
Can you think of reasons why we might want the
same denominators?
More on this next lesson?
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Practice