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In order to determine
which of these fractions
3
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is the smallest and
then the next smallest
4
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and the next smallest
and so on, like before,
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you need to express them
all with the same common
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denominator and then
compare the numerators.
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Again, the best
denominator to choose
8
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is the lowest common
multiple of the denominators.
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In this case, the lowest common
multiple of 3, 5, 7, and 8
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is 840.
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So 2/3 becomes 560/840.
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4/7 is 480/840.
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3/5 is 504 divided by 840.
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And 5/8 is 525 divided by 840.
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You can see that
4/7 is the smallest.
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3/5 is the next.
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5/8 is the next.
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And 2/3 is the largest.
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Of course, you can check your
answers on a calculator--
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if you have one.
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Here, answers are given
to three decimal places.
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2/3 is 0.667.
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4/7 is 0.571.
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3/5 is 0.600.
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And 5/8 is 0.625.
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And so again, 4/7 is the
smallest, 3/5 the next,
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5/8 the next, and
2/3 the largest.
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You can only add
fractions together
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which have the same denominator.
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So you can use your results from
the first part of this question
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to help.
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2/3 is 560/840.
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4/7 is 480/840.
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3/5 is 504/840.
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And 5/8 is 525/840.
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All the fractions now
have the same denominator.
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And so you can
add them together.
40
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This gives 560 plus 480 plus
504 plus 525, all over 840,
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which equals 2,069/840.