|
Alternatively, you can recognize that  .
So you have 
This is much faster! |
Fractions are good for canceling factors in multiplication and division. They are also the best way of exactly expressing proportions that do not have clean decimal equivalents, such as 1/7. Switch to fractions if there is a handy fractional equivalent of the decimal or percent and/or you think you can cancel a lot of factors. For example:
What is 37.5% of 240?
If you simply convert the percent to a decimal and multiply, you will have to do a fair bit of arithmetic:
|
|
Alternatively, you can recognize that .
So you have
This is much faster! |
A dress is marked up
to a final price of $140. What is the original price of the dress?
From the previous page, you know that
is equivalent to
. Thus, adding
of a number to itself is the same thing as multiplying by
:
The original price is $120.
Decimals, on the other hand, are good for estimating results or for comparing sizes. The reason is that the basis of comparison is equivalent (there is no denominator). The same holds true for percents. The implied denominator is always 100, so you can easily compare percents (of the same whole) to each other.
To convert certain fractions to decimals or percents, multiply the numerator and the denominator by the same number:
This process is faster than long division, but it only works when the denominator has only 2’s and/or 5’s as factors (as you learned earlier, fractions with denominators containing prime factors other than 2’s and 5’s will be non-terminating, and therefore cannot be represented exactly by decimals or percents).
In some cases, you might find it easier to compare a series of fractions by giving them all a common denominator, rather than by converting them all to decimals or percents. The general rule is this: Prefer fractions for doing multiplication or division, but prefer decimals and percents for doing addition or subtraction, for estimating numbers, or for comparing numbers.