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Percents
Intro
We use percents everyday. Have you ever been to the mall and found a really nice shirt with a
price tag stating it is 10% off? Or, if you are like me, shop at the clearance rack where everything
is 50% off? How about when you are at a restaurant and deciding how much tip to leave your
server?
Percent means “out of a hundred”.
We use the percent symbol, %, as a way of denoting a fraction with a denominator of 100. For
example, instead of saying, “62 out of every 100 marbles are green,” we can say, “62% of the
marbles are green”.
62
. We can then write this fraction
100
as a decimal by dividing the numerator into the denominator: 0.62. Fractions, decimals and
percents are all related,
We can write a percent as a fraction by writing it over 100:
62% →
62
→ 0.62
100
Conversions
Converting from percent to decimal:
To convert a percent into a decimal, simply divide the percentage by 100.
For example, to convert 30% into a decimal: 30 ÷ 100 = 0.3
Second example: Convert 86% into a decimal: 86 ÷ 100 = 0.86
Third example: Convert 133% into a decimal: 133 ÷100 = 1.33
Fourth example: Convert 7% into a decimal: 7 ÷ 100 = 0.07
1
Knowledge of number sense, concepts and operations.
Compare the relative values of fractions, decimals, percents and other real numbers.
1
Converting from a decimal to a percent:
To convert a decimal to a percent, simply multiply the decimal by 100.
For example, to convert 0.50 into a percentage: 0.50 x 100 = 50%
Second example: Convert 0.85 into a percentage: 0.85 x 100 = 85%
Third example: Convert 1.48 into a percentage: 1.48 x 100 = 148%
Fourth example: Convert 13.94 into a percentage: 13.84 x 100 = 138.4%
Fifth example: Convert 0.03 into a percentage: 0.03 x 100 = 3%
Converting a percent into a fraction:
To convert a percent into a fraction, simply put the percent over 100 and reduce the fraction.
For example, to convert 45% into a fraction:
45
9
, then reduce to
.
100
20
Here is a second example: Convert 68% into a fraction:
68
17
, then reduce to
.
100
25
Converting a fraction into a percent:
To convert a fraction into a percent, simply divide the numerator into the denominator and
multiply the result by 100.
For example, to convert
1
into a percent: 1 ÷ 4 = 0.25, then multiply 0.25 x 100 = 25%.
4
Another example: Convert
4
into a percent: 4 ÷ 7 = 0.571, then multiply 0.571 x 100 = 57.1%.
7
Note that sometimes your decimal will have many digits; in this case, I would round to the nearest
thousandth depending on how accurate your answer needs to be.
1
Knowledge of number sense, concepts and operations.
Compare the relative values of fractions, decimals, percents and other real numbers.
2
Using Percents
When you begin working with percent problems it is useful to
keep a few tips in mind.
1. The word “of” implies multiplication.
2. The word “what” implies the variable (usually x).
3. The word “is” implies =.
Note: Sometimes you will see the
symbol: ·
This symbol implies multiplication.
Do not confuse this symbol with a
decimal point.
3 · 2 = 6 (multiplication)
Let’s see four ways of how these are used in context.
3.2 (decimal)
Example 1: What is 15% of 400?
In order to solve this problem, let’s use our tips from above to set up an expression.
x = (0.15) · 400
Notice we re-wrote the problem as an expression we can solve. Also, the percent was converted
into a decimal. Once you write your expression, simply perform the operation:
(0.15) · 400 = 60
Therefore, 60 is 15% of 400.
Example 2: What percent of 30 is 25?
Again, let’s re-write this problem as an expression we can solve: x% · 30 = 25
To solve this problem, we need to isolate the variable x. To do this, simply divide each side of the
equal sign by 30:
x · 30 = 25
÷30
÷30
x = 0.83
0.83 · 100 = 83%
Divide both sides by 30 to isolate x.
25 ÷ 30 = 0.833
Multiply by 100 to convert into a percent.
Therefore, 83% of 30 is 25.
1
Knowledge of number sense, concepts and operations.
Compare the relative values of fractions, decimals, percents and other real numbers.
3
Example 3: 7.4 is what percent of 88.1?
Let’s rewrite as an expression: 7.4 = x% · 88.1
Next, we will solve for the value of x:
7.4 = x · 88.1
÷88.1
÷88.1
Divide both sides by 88.1 to isolate x.
0.084 = x
0.084 · 100 = 8.4%
Multiply by 100 to get a percent value.
Therefore, 7.4 is 8.4% of 88.1.
Example 4: 59 is 27% of what?
Let’s rewrite as an expression: 59 = 27% · x
Next, we will solve for the value of x:
59 = 0.27 · x
÷0.27 ÷0.27
Careful! You can not write 27; you must first convert it into a decimal, 0.27.
Divide both sides by 0.27 to isolate x.
218.5 = x
Therefore, 59 is 27% of 218.5.
In this particular example, it is important to note how the percentage must be changed into a
decimal in order to find the solution. If you forget to change the percentage into a decimal, your
answer will be off by a measure of 100.
1
Knowledge of number sense, concepts and operations.
Compare the relative values of fractions, decimals, percents and other real numbers.
4