6th Grade - Percents

Introduction

• The percent or percentage is a number, ratio, or fraction with 100 as a denominator.
• The percent means hundredths or per 100.
• A % sign denotes the percent.
• 5% means 5 out of 100.
• If you got 80% in math, you got 80 out of 100 questions correct.

Changing decimals to percents

• To change the decimal number to the percent, multiply the number by 100 or move the decimal point two places to the right and add a % sign.

Changing percents to decimals

• Remove the "%" sign and divide the number by 100 or move the decimal point to two places to the left.
• If there is no decimal, assume the decimal at the end of the number. 
• There might be a need to add a zero(s) to the front of the number for the decimal to be moved to the left.

Changing fractions to percents

• To convert a fraction to a percent, first convert the fraction to a decimal, then convert the decimal to a percent.

Changing percents to fractions

• To change percents to fractions, trade the % sign for hundredths and simplify the fraction, if possible.

Percent of a number

The following two methods can be used to determine the percent of a number:

1. Decimal Method

 25% of 40

Remove the % sign and move the decimal two places to the left.

=  0.25 X 40

= 10

2. Fraction Method

Remove the % sign and divide the number by 100.

$=\frac{25}{100}\times 40$

= 10

Examples

1) Change 0.65 to percent.

Move the decimal to two places to the right and add the % sign.

65%

2) Change 7.5 to percent.

Move the decimal to two places to the right and add the % sign.

750% 

3) Change 13.11 to percent.

Move the decimal to two places to the right and add the % sign.

1311% 

4) Change 34% to a decimal number.

Since there is no decimal point, assume the decimal point at the end and move the decimal point two places to the left.

$\frac{34}{100}=0.34$

5) Change 125% to a decimal number.

$\frac{125}{100}=1.25$

6) Change 6% to a decimal number.

Since there is no decimal point, assume the decimal point at the end and move the decimal point two places to the left.

$\frac{6}{100}=0.06$

7) Convert $\frac{3}{4}$ to percent.

$\frac{3}{4}=0.75$

Change the decimal to percent by moving the decimal point two places to the right.

0.75 = 75%

8) Convert $1\frac{1}{4}$ to percent.

$1\frac{1}{4}=\frac{5}{4}=1.25$

Change the decimal to percent by moving the decimal point two places to the right.

1.25 = 125%

9) Convert 80% to the fraction.

$80\%=\frac{80}{100}=\frac{8}{10}=\frac{4}{5}$

10) Convert 75% to the fraction.

$75\%= \frac{75}{100}=\frac{3}{4}$

11) What is 15% of 40?

a) Decimal method

Remove the % sign and move the decimal to two places left.

15% $\times$ 40

=0.15 $\times$ 40

= 6

b) Fraction method

Remove the % sign and divide the number by 100.

15% of 40

=$\frac{15}{100}\times 40$

= $\frac{600}{100}$

= 6

12. What is 250% of 50?

a) Decimal Method

250% of 50

Remove the % sign and move the decimal to two places left.

= $2.5\times 50$

= 125

b) Fraction Method

250% of 50

Remove the % sign and divide the number by 100.

= $\frac{250}{100}\times 50$

= 125

Cheat Sheet

• The word "of" means multiply.

Blunder Area

• Pay close attention to the type of problem.