Percentage Problems Practice - Calculate Discounts & Values

Master percentage calculations with step-by-step practice problems. Learn to find percentages, calculate discounts, and solve real-world percentage word problems.

๐Ÿ“šMaster Percentage Calculations with Interactive Practice
  • Calculate percentages using the fundamental formula: percentage value/initial amount = percentage/100
  • Solve discount problems to find sale prices and savings amounts
  • Find what percentage one number is of another using cross multiplication
  • Work with percentage increases and decreases in real-world scenarios
  • Convert between fractions, decimals, and percentages with confidence
  • Apply percentage formulas to word problems involving money, quantities, and measurements

Understanding Percentage

Complete explanation with examples

Formula to calculate a percentage

What is a percentage?

A percentage is a way to define a part, or fraction of a total.

When we discuss percentages, we should ask ourselves the following: "the percentage of what?". Saying 50% without specifying the whole, fails to make sense. Instead one should say " 50% 50\% of 80 80 " is 40 40 . In summary, the percentage represents what part of 100 100 is the number in question.

The percentage symbol is % \% :
When we want to express that a%a\%
We should write it as follows: a100a \over 100

In order to solve percentage problems, we apply the following formula

Percentageย valueInitialย amount=Theย percentage100 \frac{Percentage~value}{Initial~amount}=\frac{The~percentage}{100}

Percentage value: is the actual value that this percentage represents.

Initial amount: is the initial figure before being changed.
Percentage: is the percentage of change.

To solve percentage problems, we will use the following formula

You can apply this formula to any percentage exercise, as long as you note the data correctly, and verify what has been asked.


Detailed explanation

Practice Percentage

Test your knowledge with 26 quizzes

Calculate 75% of 100:

Examples with solutions for Percentage

Step-by-step solutions included
Exercise #1

Calculate 15% of 100:

Step-by-Step Solution

To find 15% of 100, you can convert the percentage to a decimal by dividing by 100:

15%=15100=0.15 15\% = \frac{15}{100} = 0.15

Next, multiply this decimal by 100:

0.15ร—100=15 0.15 \times 100 = 15

Thus, 15% of 100 is 15.

Answer:

15 15

Exercise #2

Calculate 8% of 100:

Step-by-Step Solution

To find 8% of 100, first convert the percentage to a decimal by dividing by 100:

8%=8100=0.08 8\% = \frac{8}{100} = 0.08

Then, multiply this decimal by 100:

0.08ร—100=8 0.08 \times 100 = 8

Hence, 8% of 100 is 8.

Answer:

8 8

Exercise #3

Calculate 45% of 100:

Step-by-Step Solution

To find 45% of 100, you can multiply the percentage as a decimal by the whole number. First, convert 45% into a decimal. This is done by dividing by 100: 45%=45100=0.45 45\% = \frac{45}{100} = 0.45 .

Then, multiply this decimal by 100: 0.45ร—100=45 0.45 \times 100 = 45 .

Therefore, 45% of 100 is 45 45 .

Answer:

45 45

Exercise #4

Calculate 35% of 100:

Step-by-Step Solution

To find 35% of 100, first convert the percentage into a decimal by dividing by 100: 35%=35100=0.35 35\% = \frac{35}{100} = 0.35 .

Then, multiply this decimal by 100: 0.35ร—100=35 0.35 \times 100 = 35 .

Therefore, 35% of 100 is 35 35 .

Answer:

35 35

Exercise #5

Calculate 25 over 100 as a percentage:

Step-by-Step Solution

In order to determine what percentage 25 is out of 100, we use the following formula:

Percentage=PartWholeร—100% \text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100\%

.

We begin by substituting in the known values:

Percentage=25100ร—100%=25% \text{Percentage} = \frac{25}{100} \times 100\% = 25\%

.

Thus, 25 out of 100 is 25% 25\% .

Answer:

25%

Frequently Asked Questions

What is the basic formula for calculating percentages?

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The fundamental percentage formula is: (Percentage value / Initial amount) = (The percentage / 100). This can be rearranged to solve for any missing value. For example, to find 30% of 120, you would calculate: X/120 = 30/100, then cross multiply to get X = 36.

How do I calculate a discount percentage on a sale price?

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To find a discount: 1) Multiply the percentage by the original price, 2) Divide by 100 to get the discount amount, 3) Subtract from original price. For example, a 25% discount on $200: (25 ร— 200) รท 100 = $50 discount, so final price is $200 - $50 = $150.

What's the difference between finding a percentage OF something versus finding what percentage something IS?

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Finding a percentage OF uses: (percentage/100) ร— total = result. Finding what percentage something IS uses: (part/whole) ร— 100 = percentage. For example: 20% of 50 = 10, but 10 is 20% of 50.

How do I solve percentage word problems step by step?

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Follow these steps: 1) Identify what represents 100% (the whole), 2) Identify the percentage given, 3) Determine what you're solving for, 4) Set up the proportion using the formula, 5) Cross multiply and solve. Always ask yourself 'percentage of what?' to identify the whole.

Why do I get a number higher than the original when calculating percentage increases?

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When something increases by a percentage, the result represents more than 100% of the original. For example, if a $50 item increases to $58, it's now at 116% of its original price (a 16% increase). Values above 100% indicate growth beyond the starting amount.

How do I convert fractions to percentages quickly?

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Multiply the fraction by 100. For example: 3/5 ร— 100 = 300/5 = 60%. This works because percent means 'per hundred,' so you're finding how many parts per 100 the fraction represents.

What's the trick for calculating 10%, 25%, and 50% mentally?

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Use these shortcuts: 10% = divide by 10, 25% = divide by 4, 50% = divide by 2. For other percentages, combine these: 30% = 10% ร— 3, 75% = 25% ร— 3. For example: 25% of 80 = 80 รท 4 = 20.

How do I check if my percentage calculation is correct?

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Use reverse calculation: if 30% of 120 = 36, then 36/120 ร— 100 should equal 30%. Also, sense-check your answer: 50% should be half, 25% should be one-quarter, 10% should be one-tenth of your starting number.

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