6.1 Percents, Decimals, and Fractions 503To write this as a fraction of whole numbers, we will perform the division indicated
by the fraction bar.
The fraction bar indicates division.Write as a mixed number and then multiply
by the reciprocal of 100.2
3
To simplify the fraction, factor 200 as 2 100. Then remove the
common factor of 100 from the numerator and denominator.2 100
1
1
3 100
1Multiply the numerators.
Multiply the denominators.200 1
3 100
66 23
200
3
1
100
(^66 23)
100
66
2
3
100
Self Check 5
a.Write 210% as a fraction in
simplest form.
b.Write 0.54% as a fraction in
simplest form.
Now TryProblems 39 and 435 175
535
72 100
250
525
51
EXAMPLE (^5) a.Write 175% as a fraction in simplest form.
b.Write 0.22% as a fraction in simplest form.
StrategyWe will drop the % symbol and write each given number over 100. Then
we will simplify the resulting fraction, if possible.
WHYPercentmeans parts per one hundred and the word perindicates a ratio
(fraction).
Solution
a.
Thus,.
b. Drop the % symbol and write 175 over 100.
To write this as an equivalent fraction of whole numbers,we need to move the
decimal point in the numerator two places to the right. (Recall that to find the
product of a decimal and 100, we simply move the decimal point two places to
the right.) Therefore, it follows that is the form of 1 that we should use to
build.
Thus,0.22%.
11
5,000
11
5,000
To simplify the fraction, factor 22 and 10,000.
Remove the common factor of 2 from the
numerator and denominator.2
1
11
2
15,000
22
10,000
Multiply the numerators.
Multiply the denominators.0.22 100
100 100
Multiply the fraction by a form of 1.0.22
100
0.22
100
100
100
0.22 1001001000.22%
0.22
100
175%
7
4
7
4
To simplify the fraction, prime factor 175
and 100. Remove the common factors of
5 from the numerator and denominator.5
1
51
7
2 2 5
15
1175% Drop the % symbol and write 175 over 100.