Comparing Fractions Worksheet Page 3
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2
3
4(c) Which method would you use without a calculator?
Why?
Now try to do without a calculator.
8
Method Five: Cross-Multiplication
2
4
Suppose you are given two fractions (such as
and
).
3
5
2
4
First multiply the numerator of
by the denominator of
.
3
5
2
4
Then multiply the denominator of
by the numerator of
.
3
5
Compare your two answers.
How does this tell you which of the two fractions is the lar-
ger? Explain.
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Method Six: Equivalent Fractions (Again)
Method Three is often called the method of finding a com-
1
2
mon denominator. We work out which of (say)
and
is
3
7
1
7
2
6
7
6
bigger by reasoning as follows:
=
and
=
.
>
.
3
21
7
21
21
21
1
2
So
>
.
3
7
The real-life version of this problem says Which is better,
one bottle for three or two bottles for seven? It suggests an-
other solution: One bottle for three is equivalent to getting
two bottles for six. But getting two bottles for six is better than
1
2
2
getting two bottles for seven. So
=
>
.
3
6
7
In other words, we can find a common numerator, instead of
a common denominator.
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13
Use this method to compare
and
.
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18
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