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You need to decide
which of these numbers
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is the smallest, which is
the next smallest, which
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is the next smallest,
and which is the largest.
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This is difficult, because all
the numerators are different,
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which makes it difficult
to compare the fractions.
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If you express the fractions
as equivalent fractions
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with the same
denominator, you can then
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compare the numerators to
see which are the smallest,
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and so on.
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The best numerator to choose
is the lowest common multiple
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of the numerators.
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In this case, the lowest common
multiple of 4, 6, 7, and 8
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is 168.
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This means that 168 is
the smallest number which
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4, 6, 7, and 8 all divided into,
giving a whole number result.
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To convert 7/8 to an
equivalent fraction
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with a denominator of 168,
you multiply the numerator
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and denominator by 21.
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This gives 147 over 168.
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To convert 6/7 to an
equivalent fraction
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with a denominator of 168,
you multiply the numerator
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and denominator by 24.
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This means that 6/7 is
the same as 144 over 168.
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To convert 3/4 to an
equivalent fraction
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with a denominator
of 168, you multiply
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numerator and denominator by 42.
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This means that 3/4
is 126 divided by 168.
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To convert 5/6 to an
equivalent fraction
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with a denominator of 168,
you multiply the numerator
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and denominator by 28.
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This means that 5/6
is 140 divided by 168.
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So comparing the numerators,
3/4 is fourth, 5/6 is third,
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6/7 is second, and
7/8 is the largest.
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You can always check your
answers with a calculator
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if you have one.
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Here, all answers are given
to three decimal places.
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7/8 is 0.875.
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6/7 is 0.857.
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3/4 is 0.750.
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And 5/6 is 0.833.
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So 3/4 is fourth, 5/6 is third,
6/7 is second, 7/8 is largest.
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To add these four
fractions together,
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you need to express them all
as having the same denominator.
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The denominator of a fraction
tells you what type of fraction
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you have, and you
can only add together
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things that are
of the same type.
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Here, we have 8ths, 7ths,
4ths-- or quarters-- and 6ths.
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They're all different.
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And so adding them together
doesn't make any sense.
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However, if we will express them
with the same denominator using
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the method from before,
8/7 is 147 over 168,
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6/7 is 144 over 168,
3/4 is is 126 over 168,
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and 5/6 is 140 over 168.
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As these equivalent fractions
all have the same denominator,
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you can add them together.
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This equals 147 plus
144 plus 126 plus 140,
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all divided by the common
denominator of 168.
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This equals 557 over 168.
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