# Page 3 Next Generation Arithmetic Study Guide for the ACCUPLACER® test

### Percents

The term percent means “per one hundred,” so 63% is the same as 63 out of 100 or .63 (63 hundredths), or $\frac{63}{100}$. You’ll need to know that you can substitute any of these for the other when working with percents in problems. The following lists skills that you should be able to do regarding percent.

#### Change a % to a Fraction and Back

To change a percent to a fraction, use the percent as the numerator and 100 as the denominator. Simplify the fraction if needed. For example, 25% = $\frac{25}{100}$, which can be simplified to $\frac{1}{4}$.

To change a fraction into a percent, change the fraction to an equivalent fraction with 100 as the denominator. The numerator is your percent. For example, $\frac{3}{5}$ is equivalent to $\frac{60}{100}$, so $\frac{3}{5}$ is the same as 60%.

#### Change a % to a Decimal and Back

To change a percent to a decimal, remember that a number such as 33 can be written as 33.0. Write the percent with a decimal point and then move the decimal point two places to the left. (This is the same as dividing by 100.) For 33%, first write it as 33.0 and then move the decimal two places to the left. The decimal form of 33% is 0.33.

To convert a decimal number to a percent, move the decimal two places to the right and use the % sign. 0.47 is the same as 47%.

#### Change a Fraction to a Decimal and Back

To change a fraction to a decimal, first see if can be reduced to an equivalent fraction with smaller numbers. For example, $\frac{10}{16}$ can be reduced to $\frac{5}{8}$. This makes the next step easier. A fraction represents a division problem, so to convert to the decimal do a decimal division of $numerator \div denominator$, or in this case $5 \div 8$. The answer to this division is the decimal form, 0.625.

To convert a decimal to a fraction, remember that the decimal number is given as an amount in tenths, hundredths, etc., depending on the last place of the given number. For example, 0.55 is $\frac{55}{100}$. This can be reduced to $\frac{11}{20}$, which is the correct fraction form of 0.55.

#### Calculate % Increase or Decrease

The percent increase or decrease is calculated by dividing the amount of change by the original amount. The calculation is usually done with decimal numbers and the result must then be converted to a percentage.

You can also set up a fraction with the amount of change in the numerator and the original amount in the denominator. For example, if a price was originally $80 and increases to$100, the amount of change is $20 and the original amount is$80. As a fraction, this is $\frac{20}{80}$ which is equivalent to $\frac{1}{4}$. This is the same as 0.25 or 25%. Or do $20 \div 80$ which equals 0.25 or 25%. It is worthwhile to remember a few fraction to decimal to percent equivalents, such as:

$\frac{1}{4} = 0.25 = 25\%$
$\frac{2}{4} = 0.5 = 50\%$
$\frac{3}{4} = 0.75 = 75\%$
$\frac{1}{3} = 0.33 = 33\%$
$\frac{2}{3} = 0.67 = 67\%$
$\frac{1}{5} = 0.2 = 20\%$
$\frac{2}{5} = 0.4 = 40\%$
$\frac{3}{5} = 0.6 = 60\%$
$\frac{4}{5} = 0.8 = 80\%$
$\frac{1}{10} = 0.1 = 10\%$
$\frac{3}{10} = 0.3 = 30\%$
$\frac{7}{10} = 0.7 = 70\%$
$\frac{9}{10} = 0.9 = 90\%$

#### Determine the % of a Number

To determine the percent of a number, first convert the percent to a fraction or decimal. Calculations are always done with the decimal or fractional form of the percent. Then multiply by the number. For example, to find 55% of 200, you can multiply either $0.55 \times 200$ or $\frac{55}{100} \times 200$. The answer is 110.

#### Apply % to Real-Life Contexts

The most common real-life example of percentages is in prices. Sales are usually given as a percent. A 20% sale means 20% off of the usual price. If you want to know how much you are saving, multiply 0.2 or $\frac{2}{10}$ by the original price.

To find the sale price, subtract the amount you saved from the original price. For example, if a $50 item is on sale at %20 off, you save 0.2 x$50, or $10, and the sale price is$50 - $10, or$40.