A. When comparing fractions, we often need to know which fraction is smaller or larger.
a c
Note: You can use
cross-multiplication to determine which
b d fraction is smaller or larger.
ad ? bc
In other words, if ad > bc then the fraction on the left
a c
is larger. If ad < bc, then the fraction on the right is
b d
larger.
If ad = bc, then the 2 fractions are equivalent.
5
7
Ex [1] Which is greater: 6 or 9 ?
a) Using the rule of cross-multiplication we can compare 9 x 5 and 6 x 7.
b) 9 x 5 = 45.
c) 6 x 7 = 42.
d) Since 45 > 42, the fraction on the left is greater.
e)
So the answer is 5/6.
B. Sometimes instead of giving two fractions, the problem will give one fraction and one decimal. In problems like these, simply change the decimal to a fraction (it does not have to be in simplest terms) and compare using this method.
Ex [1] Which is smaller: .54 or 6 ?
11
a) You can change .54 to 54/100 (there is no need to simplify).
b) Using cross-multiplication we can compare 54 x 11 and 6 x 100.
c) 54 x 11 = 594 (Click here to learn how to multiply by 11).
d) 6 x 100 = 600.
e) Since 594 < 600, the fraction (or in this case the decimal) on the left is smaller.
f) The answer is .54.
C. In problems like Ex [1] Part B, it would be faster if you knew that 6/11= .5454... Therefore, memorizing the fractions here will be useful in situation like these.