The above can be expressed as: “The ratio of sugar to salt to water is 3 to 2 to 4.”
Ratios can be represented in a few different ways:
■ The word to 3 to 4
■ Using a colon 3: 4■ As a fraction (^34)
The Elements of a Ratio
The relationship that a ratio specifies will be either part-to-part or part-to-whole.
An example of a part-to-part ratio is “In a school, there are 7 boys for every 3 girls.”
An example of a part-to-whole ratio is “In a school, there are 7 boys for every 10
students.”
It is important to note that you can derive a part-to-whole ratio from a
part-to-part ratio, and vice versa. If the ratio of boys to girls in a school is
7:3, then the ratio of boys to all students is 7:10.
Ratios Do Not Specify Amounts!
It is important to remember that a ratio only provides a relationship between
quantities, not the actual amounts of each quantity. If the ratio of boys to girls is
7:3, there can be any number of values for boys and girls, as long as those values
satisfy the given ratio.
Expressing Ratios
As discussed previously, there are several ways of expressing ratios. For the purpose
of the GRE, the best way to express a ratio between two quantities is as a fraction.
But before doing so, you must label the units.
If you are told that the ratio of men to women is 1:3, then on your paper, you
should label which quantity corresponds with the numerator of the fraction and
which quantity corresponds with the denominator of the fraction:
m men
w women =
1
3
To make the quantities easier to work with algebraically, it’s even better to write:
m
w =
1
3 , where m = the number of men and w = the number of women
Proportions
The simplest types of ratio questions will give you a ratio and the value for one
quantity and will ask you to find a value for the other quantity. Whenever you have
a ratio with the value for one quantity, set up a proportion.
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