Math 6 Honors Periods 6 & 7

Percent and Fractions 9-1

The word “percent” is derived from the Latin “per centum” meaning “per hundred” or “out of one hundred” so 28% means 28 out of 100

A percent is a ratio that compares a number to 100. Therefore you can write a percent as a fraction with a denominator of 100, so 28% is also 28/100

Our book’s example is as follows;

During basketball season, Alice made 17 out of 25 free throws, while Nina made 7 out of 10. To see who did better, we compare the fractions representing each girl’s successful free throws.

17/27 or 7/10 or

In comparing fractions it is often convenient to use the common denominator 100, even if 100 is not the LCD of the fractions.

17. 4 = 68 thithithiett7.10=70
24^t4th100thiethithei10t10t100

Since Alice makes 68 free throws per 100 and Nina makes 70 per hundred, Nina is the better free throw shooter.

the ratio of a number to 100 is called a percent. We write percents by using the symbol %

so

17/25=68% and 7/10= 70%

Rule

To express the fraction a/b as a percent, solve the equation

n/100 = a/b

for the variable n and write n%

Just set up as a ratio and compare your fraction to 100. You know three out of the four numbers. Express 17/40 as a percent

Use the proportion method or just divide 17 by 40 multiply both sides by 100

n= 42½

Therefore, 17/40 = 42.5%

Rule

To express n% as a fraction, write the fraction

n/100 in lowest terms

Express 7 1/2 % as a fraction in lowest terms

7 ½ % = 7.5% = 7.5/100 How do we get rid of the decimal? multiply numerator and denominator by ten

7.5 . 10 = 75 simplify
100 t10 t1000

=3/40

Since a percent is the ratio of a number to 100, we can have percents that are greater than or equal to 100%

100 = 100%
100

165 =165%
100

Write 250% as a mixed number in simple form

250% =

250=
100

2 50/100 = 2 1/2

Percents and Decimals 9-2

By looking at the following examples, you will be able to see a general relationship between decimals and percents

51% = 47/100 = 0.57 113% = 113/100 = 1.13

0.79 = 79/100 = 79% .06 = 6/100 = 6%

Rules

To express a percent as a decimal, move the decimal point two places to the left and remove the percent sign

57% = 0.57 thith 113% = 1.13

To express a decimal as a percent, move the decimal point two places to the right and add a percent sign

0.79 = 79% thithith0.06 = 6%

Express each percent as a decimal ( remember- the decimal is so sad to see the % leave that it runs away – two places to the left—from where it was)

1. 83.5% = 0.835

2. 450% = 4.5

3. .25% = 0.0025

Express each decimal as a percent [careful] ( remember- the decimal is so happy to see the % that it runs ( 2 place to the right) towards the %)

1. 10.5 = 1050.%

2. 0.0062 = 0.62%

3. 0.574= 57.4%

In 9-1 you learned one method of changing a fraction into a percent. Here is an alternative method

Rule

To express a fraction as a percent, first express the fraction as a decimal

and then as a percent

Express 7/8 as a percent

Divide 7 by 8

7/8

= 0.875 = 87.5%

Express 1/3 as a percent to the nearest tenth of a percent

divide 1 by 3

1/3

since this becomes a repeating decimal

.33333333….

or .3 with a vinculum, we write 1/3 as

33 1/3%