This ensemble of printable percentage worksheets is tailor-made for students of grade 6, grade 7, and grade 8. A plethora of exercises like finding the percent of the shaded region, finding percent of a whole numbers and decimals, comparing quantities, well-researched word problems and a lot more are available here. The pdf worksheets are split into metric and customary units to enable convenient downloads. Access some of these worksheets for free!
The Meaning of Percentages. Percentage is a term from Latin, meaning ‘out of one hundred’. You can therefore consider each ‘whole’ as broken up into 100 equal parts, each one of which is a single percent. Cent is an old European word with French, Latin, and Italian origins meaning “hundred”. So, percent is translated directly to “per hundred.” If you have 87 percent, you literally have 87 per 100. If it snowed 13 times in the last 100 days, it snowed 13 percent of the time. Percentage definition is - a part of a whole expressed in hundredths. How to use percentage in a sentence. Percentage is a term from Latin, meaning ‘out of one hundred’. You can therefore consider each ‘whole’ as broken up into 100 equal parts, each one of which is a single percent. The box below shows this for a simple grid, but it works the same way for anything: children in a class, prices, pebbles on the beach, and so on.
Engage in this series of base 10 blocks worksheets that contain nine problems per page. Discern and count the shaded squares to determine the percentage of the shaded area.
Keenly observe the shaded region of the shapes provided. Find the percentage of the shaded area in each problem.
Each 6th grade worksheet contains 14 problems calculating the percentage of whole numbers. Use the answer keys to verify your responses.
Calculate the amount for each base value in these worksheets that contain units of measurement. Also, solve the percent word problems based on interesting real-life scenarios.
Find the value that constitutes an equivalent percentage for each decimal and round them to the nearest hundredth.
Work out the percentages. Then, compare them and insert the appropriate <, > or = symbols in the boxes. Word problems are also furnished to help learners grasp the concept of comparing quantities.
Based on the number line models provided, fill in the boxes with either the appropriate percentages or numbers. These printable worksheets form a great visual aid for 6th grade and 7th grade students in understanding percentages.
Read each question carefully to find the unknown percentages, base values or amounts. Round your answers to the nearest hundredth.
Based on the original amount, find the ratio of change in quantity. Then, calculate the percentage of increase or decrease. Each worksheet includes a number of word problems suitable for 7th grade and 8th grade students.
Find the increase or decrease in amount using the given percentage. Add or subtract the amount so derived to determine the change in quantity. A few word problems are incorporated here for variety.
Engage this set of printable worksheets that include an assortment of exercises based on conversion between fractions, decimals and percent.
(37 Worksheets)
Related Worksheets
»Proportions
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Calculator Use
Find a percentage or work out the percentage given numbers and percent values. Use percent formulas to figure out percentages and unknowns in equations. Add or subtract a percentage from a number or solve the equations.
How to Calculate Percentages
There are many formulas for percentage problems. You can think of the most basic as X/Y = P x 100. The formulas below are all mathematical variations of this formula.
Let's explore the three basic percentage problems. X and Y are numbers and P is the percentage:
- Find P percent of X
- Find what percent of X is Y
- Find X if P percent of it is Y
Read on to learn more about how to figure percentages.
1. How to calculate percentage of a number. Use the percentage formula: P% * X = Y
Example: What is 10% of 150?
- Convert the problem to an equation using the percentage formula: P% * X = Y
- P is 10%, X is 150, so the equation is 10% * 150 = Y
- Convert 10% to a decimal by removing the percent sign and dividing by 100: 10/100 = 0.10
- Substitute 0.10 for 10% in the equation: 10% * 150 = Y becomes 0.10 * 150 = Y
- Do the math: 0.10 * 150 = 15
- Y = 15
- So 10% of 150 is 15
- Double check your answer with the original question: What is 10% of 150? Multiply 0.10 * 150 = 15
2. How to find what percent of X is Y. Use the percentage formula: Y/X = P%
Example: What percent of 60 is 12?
- Convert the problem to an equation using the percentage formula: Y/X = P%
- X is 60, Y is 12, so the equation is 12/60 = P%
- Do the math: 12/60 = 0.20
- Important! The result will always be in decimal form, not percentage form. You need to multiply the result by 100 to get the percentage.
- Converting 0.20 to a percent: 0.20 * 100 = 20%
- So 20% of 60 is 12.
- Double check your answer with the original question: What percent of 60 is 12? 12/60 = 0.20, and multiplying by 100 to get percentage, 0.20 * 100 = 20%
3. How to find X if P percent of it is Y. Use the percentage formula Y/P% = X
Example: 25 is 20% of what number?
- Convert the problem to an equation using the percentage formula: Y/P% = X
- Y is 25, P% is 20, so the equation is 25/20% = X
- Convert the percentage to a decimal by dividing by 100.
- Converting 20% to a decimal: 20/100 = 0.20
- Substitute 0.20 for 20% in the equation: 25/0.20 = X
- Do the math: 25/0.20 = X
- X = 125
- So 25 is 20% of 125
- Double check your answer with the original question: 25 is 20% of what number? 25/0.20 = 125
Remember: How to convert a percentage to a decimal
- Remove the percentage sign and divide by 100
- 15.6% = 15.6/100 = 0.156
Remember: How to convert a decimal to a percentage
- Multiply by 100 and add a percentage sign
- 0.876 = 0.876 * 100 = 87.6%
Percentage Problems
There are nine variations on the three basic problems involving percentages. See if you can match your problem to one of the samples below. The problem formats match the input fields in the calculator above. Formulas and examples are included.
What is P percent of X?
- Written as an equation: Y = P% * X
- The 'what' is Y that we want to solve for
- Remember to first convert percentage to decimal, dividing by 100
- Solution: Solve for Y using the percentage formula
Y = P% * X
Example: What is 10% of 25?
- Written using the percentage formula: Y = 10% * 25
- First convert percentage to a decimal 10/100 = 0.1
- Y = 0.1 * 25 = 2.5
- So 10% of 25 is 2.5
Y is what percent of X?
- Written as an equation: Y = P% ? X
- The 'what' is P% that we want to solve for
- Divide both sides by X to get P% on one side of the equation
- Y ÷ X = (P% ? X) ÷ X becomes Y ÷ X = P%, which is the same as P% = Y ÷ X
- Solution: Solve for P% using the percentage formula
P% = Y ÷ X
Example: 12 is what percent of 40?
- Written using the formula: P% = 12 ÷ 40
- P% = 12 ÷ 40 = 0.3
- Convert the decimal to percent
- P% = 0.3 × 100 = 30%
- So 12 is 30% of 40
Y is P percent of what?
- Written as an equation: Y = P% * X
- The 'what' is X that we want to solve for
- Divide both sides by P% to get X on one side of the equation
- Y ÷ P% = (P% × X) ÷ P% becomes Y ÷ P% = X, which is the same as X = Y ÷ P%
- Solution: Solve for X using the percentage formula
X = Y ÷ P%
Example: 9 is 60% of what?
- Writen using the formula: X = 9 ÷ 60%
- Convert percent to decimal
- 60% ÷ 100 = 0.6
- X = 9 ÷ 0.6
- X = 15
- So 9 is 60% of 15
What percent of X is Y?
- Written as an equation: P% * X = Y
- The 'what' is P% that we want to solve for
- Divide both sides by X to get P% on one side of the equation
- (P% * X) ÷ X = Y ÷ X becomes P% = Y ÷ X
- Solution: Solve for P% using the percentage formula
P% = Y ÷ X
Example: What percent of 27 is 6?
- Written using the formula: P% = 6 ÷ 27
- 6 ÷ 27 = 0.2222
- Convert decimal to percent
- P% = 0.2222 × 100
- P% = 22.22%
- So 22.22% of 27 is 6
P percent of what is Y?
- Written as an equation: P% × X = Y
- The 'what' is X that we want to solve for
- Divide both sides by P% to get X on one side of the equation
- (P% × X) ÷ P% = Y ÷ P% becomes X = Y ÷ P%
- Solution: Solve for X using the percentage formula
X = Y ÷ P%
Example: 20% of what is 7?
- Written using the formula: X = 7 ÷ 20%
- Convert the percent to a decimal
- 20% ÷ 100 = 0.2
- X = 7 ÷ 0.2
- X = 35
- So 20% of 35 is 7.
P percent of X is what?
- Written as an equation: P% * X = Y
- The 'what' is Y that we want to solve for
- Solution: Solve for Y using the percentage formula
Y = P% * X
Example: 5% of 29 is what?
- Written using the formula: 5% * 29 = Y
- Convert the percent to a decimal
- 5% ÷ 100 = 0.05
- Y = 0.05 * 29
- Y = 1.45
- So 5% of 29 is 1.45
Y of what is P percent?
- Written as an equation: Y / X = P%
- The 'what' is X that we want to solve for
- Multiply both sides by X to get X out of the denominator
- (Y / X) * X = P% * X becomes Y = P% * X
- Divide both sides by P% so that X is on one side of the equation
- Y ÷ P% = (P% * X) ÷ P% becomes Y ÷ P% = X
- Solution: Solve for X using the percentage formula
X = Y ÷ P%
Example: 4 of what is 12%?
How To Understand Percentages Easy
- Written using the formula: X = 4 ÷ 12%
- Solve for X: X = Y ÷ P%
- Convert the percent to a decimal
- 12% ÷ 100 = 0.12
- X = 4 ÷ 0.12
- X = 33.3333
- 4 of 33.3333 is 12%
What of X is P percent?
- Written as an equation: Y / X = P%
- The 'what' is Y that we want to solve for
- Multiply both sides by X to get Y on one side of the equation
- (Y ÷ X) * X = P% * X becomes Y = P% * X
- Solution: Solve for Y using the percentage formula
Y = P% * X
Example: What of 25 is 11%?
- Written using the formula: Y = 11% * 25
- Convert the percent to a decimal
- 11% ÷ 100 = 0.11
- Y = 0.11 * 25
- Y = 2.75
- So 2.75 of 25 is 11%
Y of X is what percent?
- Written as an equation: Y / X = P%
- The 'what' is P% that we want to solve for
- Solution: Solve for P% using the percentage formula
P% = Y / X
Example: 9 of 13 is what percent?
Percentages
- Written using the formula: P% = Y / X
- 9 ÷ 13 = P%
- 9 ÷ 13 = 0.6923
- Convert decimal to percent by multiplying by 100
- 0.6923 * 100 = 69.23%
- 9 ÷ 13 = 69.23%
- So 9 of 13 is 69.23%
Related Calculators
Find the change in percentage as an increase or decrease using the Percentage Change Calculator.
Solve decimal to percentage conversions with our Decimal to Percent Calculator.
Convert from percentage to decimals with the Percent to Decimal Calculator.
If you need to convert between fractions and percents see our Fraction to Percent Calculator, or our Percent to Fraction Calculator.
References
Weisstein, Eric W. 'Percent.' From MathWorld -- A Wolfram Web Resource.