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You need to decide which
of these three fractions
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is the smallest, the middle
sized, and the largest.
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5
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In order to do
this, you will need
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to express the fractions
as equivalent fractions
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with the same
denominator, and then
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compare the new numerators.
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The denominator to choose is
the lowest common multiple.
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And the lowest common
multiple of 5, 7, and 8
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which are the three denominators
in the fractions, is 280.
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This means that
280 is the smallest
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number that 5, 7, and
8 all divided into,
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given a whole number solution.
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To convert 3/5 into
an equivalent fraction
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with a denominator of 280,
you multiply the numerator
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and denominator by 56.
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This means that 3/5 is the
same as 168 divided by 280.
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To convert 4/7 to an
equivalent fraction
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with a denominator of 280,
you multiply the numerator
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and denominator by 40.
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This means that 4/7 is the
same as 160 divided by 280.
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To convert 5/8 to an
equivalent fraction
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with a denominator
of 280, you multiply
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numerator and denominator by 35.
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This means that 5/8
is 175 divided by 280.
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Now, looking at these
three new fractions
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you can see that
4/7 is the smallest,
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3/5 is the next smallest,
and 5/8 is the biggest.
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You could always
use a calculator
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to check your answer,
if you have one.
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Here, all answers are given
to three decimal places,
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3/5 is 0.600.
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4/7 is 0.571, and 5/8 is 0.625.
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So again, 4/7 is the
smallest, 3/5 is the next,
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and 5/8 is the biggest.
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In order to add
fractions together
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you need to have fractions
with equivalent denominators,
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or a so-called
common denominator.
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This is because you
can only add together
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things that are the
same, and the denominator
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tells you what type
of fraction you have.
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Here, we have 5ths
and 7ths at 8ths.
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And they're all different.
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However, you can use the
method from the question
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before to express them
as equivalent fractions
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with denominators of 180.
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So 3/5 is 168/280, 4/7 is
160/280, and 5/8 is 175/280.
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As these three new fractions
have the same denominator,
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you can add them together.
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This gives 168 plus 160 plus 175
all over the common denominator
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of 280, which is 503/280.
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