I. Intro
Percent is a ratio or proportion per hundred (out of hundred). More simply stated, percent (per cent) means "per 100" and is expressed as a number followed by a percent sign (%).Here is a visual representation of a grid that has 100 boxes in total of which 77 are colored. Hence, 77% of the boxes are colored.
II. Converting Between Percents, Fractions & Decimals
A. Converting Percents to Fractions
A percent is a way of expressing a fraction were the number to the left of the % sign is the numerator and 100 is the denominator. For example, 77% = 77/100. 109% = 109/100.
To convert to a fraction
1) write the percent over 100 and drop the % sign.
2) reduce if necessary.
Example:
30% = 30/100 = 3/10
B. Converting Fractions to Percents
1. The easiest way to make this conversion is to first convert the fraction to a decimal and then convert the decimal to a percentage.
1) Divide the numerator by the denominator.
2) Multiply the result by 100 (aka move decimal to the right two spaces) and add the %
Example: Convert 3/8 to a percentage
3/8 = 0.375
0.375 x 100 = 37.5
add % sign: 37.5%
2. Another option is to convert the fraction into one with a denominator of 100, then write the answer as a percent.
1) Find a number you can multiply the bottom of the fraction by to get 100.
2) Multiply both top and bottom of the fraction by that number.
3) Then write down just the top number with the "%" sign.
Example: Convert 3/4 to a percent
4 x 25 = 100 so
3/4 x 25/25 = 75/100 = 75%
C. Converting Percents to Decimals
To convert a percent to a decimal, simply divide by 100 and remove the % sign. The result of dividing by 100 simply move the decimal 2 places to the left.
Example: Convert 30% to a decimal
Remove the % from 30%
30/100 = 0.3
or use the easy method by simply taking 30% and moving the decimal point two places to the left and removing the % sign giving you 0.3
D. Converting Decimals to Percents
To convert a decimal to a percent, simply multiply by 100 and add the % sign. Multiplying by 100 simply moves the decimal point 2 places to the right.
Example: Convert 0.125 to a percent
0.125 x 100 = 12.5
add the % sign: 12.5%
or use the easy method by simply taking 0.125 and moving the decimal point two places to the right and adding the % sign giving you 12.5%
III. Finding the Percent of a Number
To find the percent of a number, simply change the percent into a decimal or fraction, then multiply by the number.
Example: What is 18% of 150?
18% = .18
.18 x 150 = 27
or using fraction method
18% = 18/100 = 9/50
9/50 x 150/1 = 1350/50 = 27
Quick/mental percentage calculations
-Finding 100% of a number: 100% means the whole thing so 100% of a number is the number.
100% of 91 = 91
-Finding 10% of a number: This can be quickly calculated by simply moving the decimal point of the number one place to the left.
10% of 91 = 9.1
-Finding 1% of a number: Solve by moving the decimal point of the number two places to the left.
1% of 91 = 0.91
-Finding 50% of a number: As 100% is a whole, 50% is half the number.
50% of 91 = 45.5
-Finding 20% of a number: First find 10% of the number, then double the number.
20% of 91 = 10% of 91 times 2 = 9.1 times 2 = 18.2
IV. Percentage Change
% change = [(new value - old value)/old value)] x 100
Step 1: $5 to $6 is a $1 increase
Step 2: Divide by the old value: $1/$5 = 0.2
Step 3: Convert 0.2 to percentage: 0.2×100 = 20% rise
To convert a percent to a decimal, simply divide by 100 and remove the % sign. The result of dividing by 100 simply move the decimal 2 places to the left.
Example: Convert 30% to a decimal
Remove the % from 30%
30/100 = 0.3
or use the easy method by simply taking 30% and moving the decimal point two places to the left and removing the % sign giving you 0.3
D. Converting Decimals to Percents
To convert a decimal to a percent, simply multiply by 100 and add the % sign. Multiplying by 100 simply moves the decimal point 2 places to the right.
Example: Convert 0.125 to a percent
0.125 x 100 = 12.5
add the % sign: 12.5%
or use the easy method by simply taking 0.125 and moving the decimal point two places to the right and adding the % sign giving you 12.5%
III. Finding the Percent of a Number
To find the percent of a number, simply change the percent into a decimal or fraction, then multiply by the number.
Example: What is 18% of 150?
18% = .18
.18 x 150 = 27
or using fraction method
18% = 18/100 = 9/50
9/50 x 150/1 = 1350/50 = 27
Quick/mental percentage calculations
-Finding 100% of a number: 100% means the whole thing so 100% of a number is the number.
100% of 91 = 91
-Finding 10% of a number: This can be quickly calculated by simply moving the decimal point of the number one place to the left.
10% of 91 = 9.1
-Finding 1% of a number: Solve by moving the decimal point of the number two places to the left.
1% of 91 = 0.91
-Finding 50% of a number: As 100% is a whole, 50% is half the number.
50% of 91 = 45.5
-Finding 20% of a number: First find 10% of the number, then double the number.
20% of 91 = 10% of 91 times 2 = 9.1 times 2 = 18.2
Or
IV. Percentage Change
Percentage change is the relative change between an old value and its new value, expressed as a percentage of the old value
The process for finding percentage change is:
The process for finding percentage change is:
1. Subtract the old value from the new value.
2. Divide this by the old value
3. Convert to a percentage (Multiple by 100 and add the % symbol)
Example 1:
A pair of socks went from $5 to $6, what is the percentage change?Step 1: $5 to $6 is a $1 increase
Step 2: Divide by the old value: $1/$5 = 0.2
Step 3: Convert 0.2 to percentage: 0.2×100 = 20% rise
Example 2
The price of a toy car is decreased from $20 to $15 after a discount. Find the percentage change in the amount.Using the formula:
= [(15 - 20)/20] x 100
=-5/20 x 100
=-25%
Practice
