Basic Mathematics for College Students

6.1 Percents, Decimals, and Fractions 501

figure is notshaded by subtracting the percent of the figure that is shaded from 100%.

So 7% of the figure is notshaded.
To illustrate a percent greater than 100%, say 121%, we would shade one entire
figure and 21 of the 100 square regions in a second, equal-sized grid.

100%93%7%

100% 21% 121%

EXAMPLE (^1) Tossing a Coin A coin was tossed 100 times and it landed
heads up 51 times.
a.What percent of the time did the coin land heads up?
b.What percent of the time did it land tails up?
StrategyWe will write a fraction that compares the number of times that the coin
landed heads up (or tails up) to the total number of tosses.
WHYSince the denominator in each case will be 100, the numerator of the
fraction will give the percent.
Solution
a.If a coin landed heads up 51 times after being tossed 100 times, then
of the time it landed heads up.
b.The number of times the coin landed tails up is times. If a coin
landed tails up 49 times after being tossed 100 times, then
of the time it landed tails up.

49

100

 49 %

100  51  49

51

100

 51 %

Self Check 1

BOARD GAMESA standard

Scrabble game contains 100 tiles.

There are 42 vowel tiles, 2 blank

tiles, and the rest are consonant

tiles.

a.What percent of the tiles are

vowels?

b.What percent of the letter

tiles are consonants?

Now TryProblem 13

2 Write percents as fractions.

We can use the definition of percent to write any percent in an equivalent fraction form.

Writing Percents as Fractions

To write a percent as a fraction, drop the % symbol and write the given

number over 100. Then simplify the fraction, if possible.

EXAMPLE (^2) Earth The chemical makeup of Earth’s atmosphere is 78%
nitrogen, 21% oxygen, and 1% other gases. Write each percent as a fraction in
simplest form.
StrategyWe will drop the % symbol and write the 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).
Self Check 2
WATERMELONSAn average
watermelon is 92% water. Write
this percent as a fraction in
simplest form.
Now TryProblems 17 and 23