Percent

Here is everything you need to know about percentages. You’ll learn how to find the percent of a number, how to calculate with percent multipliers, and how to increase and decrease a number by a percent. You’ll also learn about percent changes.

Students will first learn about percents as part of ratios and proportional relationships in 6th grade.

What is a percent?

A percent is a number that is expressed as a fraction of 100. To do this, you need to know that “percent” means “number of parts per hundred.” The symbol we use for percent is the percent sign \%.

There are different types of questions involving percents.

How to find a percent of a number

This is when you are asked to find a certain percentage of an amount.

For example,

find 25\% of \$32.

This is the same as finding a \cfrac{1}{4} of \$32.

The answer is \$8.

You can also write the percent as a fraction (\cfrac{25}{100}) and then multiply the fraction by the total amount (32).

Step-by-step guide: Percent of a number

Percent conversions

Percents, fractions, and decimals can all be used to represent part of a whole.

For example,

It is useful to be able to convert between percents, fractions, and decimals.

To change a percent into a fraction, write the percent as the numerator of a fraction and 100 as the denominator, and then simplify the resulting fraction if possible.

For example,

To change a fraction into a percent, there are two methods.

Method 1 : First, see if it is possible to write an equivalent fraction with a denominator of 100. If so, the numerator will be the percent.

For example,

Method 2 : Carry out the division represented in the fraction and then multiply by 100.

For example,

To change a percent into a decimal, divide the percent number by 100.

For example,

To change a decimal into a percent, multiply the decimal by 100.

For example,

Percent as operator

In order to find a percent of an amount, a percent increase, or a percent decrease, you can use a percent multiplier.

To do this, you change the percent that you want into a decimal, then multiply the amount by that decimal to calculate the answer.

For example,

34\% of 58.

Here you want \bf{34\%}, which as a decimal is \bf{0.34}.

Therefore, the calculation is:

For example,

Increase 78 by 15\%.

Here you want an increase of 15\% , which means in total you want \bf{115\%}.

This is because you want another 78 \, (100\%) plus another 15\% of 78 \, ( + 15\%).

115\% as a decimal is \bf{1.15}.

Therefore, the calculation is:

For example,

Decrease 45 by 20\%.

Here you want a decrease of 20\%, which means in total you want \bf{80\%}.

Since you want to decrease 45 by 20\%, that means you need to determine 80\% of 45. \, 80\% as a decimal is \bf{0.8}.

Therefore, the calculation is:

Percent increase

This is when you are asked to increase (make bigger) a value by a certain amount.

For example,

increase 40 \, g by 10\%.

You can find 10\% and add it on.

10\% of 40 is 4.

The answer is 44 \, g.

Step-by-step guide: Percent increase

Percent decrease

This is when you are asked to decrease (make smaller) a value by a certain amount.

For example,

decrease 60 \, kg by 10\%.

You can find 10\% and subtract it.

10\% of 60 is 6.

The answer is 54 \, kg.

Step-by-step guide: Percent decrease

Step-by-step guide: Percent increase and decrease

Percent change

When values change, you can express this change as a percent of the original value.

For example,

work out the percent change of 26 \, kg from 25 \, kg.

The answer is 4\%.

Step-by-step guide: Percent change

Percent error

This is when you find the difference between an estimated value and the exact or known value. The difference is then divided by the known value and multiplied by 100\%.

For example,

I estimated that 200 people would attend the concert, but 250 people attended.

Step-by-step guide: Percent error

Simple interest

This is when you find the percent of an original amount and multiply it by the time period of the investment.

Simple interest = principal amount × rate of interest × time period

For example,

calculate the interest earned on \$3,000 with a simple interest rate of 5\% over 2 years.

Step-by-step guide: Simple interest

Reverse percents

This is when you are given a certain percent of a number and you have to find the original number.

For example,

20\% of a number is 6, what is the number?

To find the original number you need to find 100\% or “one whole.”

The answer is 30.

Percent calculations

Let’s look at different methods that can be used to perform percent calculations.

For example,

what is 40\% of 70?

Method 1: The one percent method

Find 1\% first by dividing the amount by 100 and then multiply the amount by the percent you want.

Method 2: The decimal multiplier method

Write the percent you want as a decimal and then multiply the amount by this decimal.

Method 3: Using equivalent fractions

Write the percent you want as a fraction in simplest form and then multiply the amount by this fraction.

Method 4: Building up an answer from simple percent you know

Using simple percents, you can build up the answer to the question.

For this question, if you know 10\% of 70, you can multiply this answer by 4 to find 40\%.

10\% of 70 = 7

40\% of 70 = 7 \times 4 = 28

Note, methods 1 and 2 lend themselves best to questions where you are allowed to use a calculator. Methods 3 and 4 are most helpful when calculators are not permitted.

What is a percent?

Common Core State Standards

How does this relate to 6th grade math?

• 6th grade – Ratios and Proportional Relationships (6.RP.3c)
  Find a percent of a quantity as a rate per 100 (for example, 30\% of a quantity means \frac{30}{100} times the quantity); solve problems involving finding the whole, given a part and the percent.

How to find the percent

In order to work out percents, you need to be clear about what you have and what you are trying to find out. Percent questions can vary and there will be links in the other sections with more details.

1. Write down what you have and what you are trying to find.
2. Work out what you need.
3. Write down the final answer.

Percent examples

Example 1: percent of a number

Find 23\% of \$160.

1. Write down what you have and what you are trying to find.

100\% is \$160.

You need to find 23\% of \$160.

2Work out what you need.

Using the one percent method:

3Write down the final answer.

23\% of \$160 is \bf{\$36.80}.

Example 2: percent multipliers

Find 39\% of \$4,700.

Example 3: percent increase

Increase \$200 by 30\%.

Example 4: percent decrease

Decrease 700 \, g by 20\%.

Example 5: percent change

A t-shirt went from \$10 to \$12. Work out the percent change.

Example 6: reverse percent

A coat costs \$40 after a 20\% price cut. Find the original price.

Teaching tips for percent

• If needed, provide students with hundreds grids to help them understand percent. This will provide them with a visual of 100 and they can fill in squares to represent the percents.

• Provide students with real-world examples and situations as often as possible. This will help them gain a deeper understanding of the content.

• Create an anchor chart to display in the classroom showing each type of percent problem for students to refer to when needed.

Easy mistakes to make

• Money needs two digits for the cents
  Find 34\% of \$620.
  620\times0.34=210.8
  The answer is \$210.80.

• The decimal multiplier to work out a percent increase can be greater than \bf{1}
  Increase 50 \, km by 3\%.
  We can find 103\%.
  50\times1.03 =51.5
  The answer is 51.5 \, km.

• Percents can be greater than \bf{100\%}
  Calculate the percent change of 450 from 200.
  The percent change 450-200=250.
  
  \cfrac{250}{200}\times100=125
  
  So the percent change of 450 from 200 is 125\%.

The next lessons are

• Compound measures
• Converting fractions, decimals, and percentages
• Exponents
• Algebraic expressions
• Compound interest formula
• Exponential decay

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