# Percents

Problems involving percent are common on the SAT. The word

*percent*means “divided by one hundred.” When you see the word “percent,” or the symbol %, remember it means . For example,25 percent

To convert a decimal into a percent, move the decimal point two places to the right.

For example,

0.25 = 25%

0.023 = 2.3%

1.3 = 130%

Conversely, to convert a percent into a decimal, move the decimal point two places to the left.

For example,

47% = .47

3.4% = .034

175% = 1.75

To convert a fraction into a percent, first change it into a decimal (by dividing the denominator [bottom] into the numerator [top]) and then move the decimal point two places to the right.

For example,

For example,

Conversely, to convert a percent into a fraction, first change it into a decimal and then change the decimal into a fraction.

For example,

For example,

Following are the most common fractional equivalents of percents:

**Note:**Percent problems often require you to translate a sentence into a mathematical equation.

Example-1

*What percent of 25 is 5?*

*10%**20%**30%**35%**4**0%*

Solution

Translate the sentence into a mathematical equation as follows:

What | percent | of | 25 | is | 5 |

x |
. |
25 | = | 5 |

*x* = 20

The answer is (B).

Example-2

*2 is 10% of what number*

- A. 10
- B. 12
- C. 20
- D. 24
- E.
*32*

Solution

Translate the sentence into a mathematical equation as follows:

2 | is | 10 | % | of | what number |

2 | = | 10 | . | x |

20 = *x*

The answer is (C).

Example-3

*What percent of a is 3a ?*

*100%**150%**200%**300%**3**50%*

Solution

Translate the sentence into a mathematical equation as follows:

What | percent | of | a |
is | 3a |

x |
. |
a |
= | 3a |

(by canceling the *a*’s)

*x* = 300

The answer is (D).

Example-4

*If there are 15 boys and 25 girls in a class, what percent of the class is boys?*

*10%**15%**18%**25%**37**.5%*

Solution

The total number of students in the class is 15 + 25 = 40. Now, translate the main part of the sentence into a mathematical equation:

what | percent | of | the class |
is | boys |

x |
. |
40 | = | 15 |

2*x* = 75

*x* = 37.5

The answer is (E).

**Note:**Often you will need to find the percent of increase (or decrease). To find it, calculate the increase (or decrease) and divide it by the original amount:

**Percent of change:**

Example-5

*The population of a town was 12,000, and ten years later it was 16,000. What was the percent increase in the population of the town during this period?*

*50%**75%**80%**1**20%*

Solution

The population increased from 12,000 to 16,000.

Hence, the change in population was 4,000.

Now, translate the main part of the sentence into a mathematical equation:

Percent of change:

Percent of change:

The answer is (A).