Percentage Practice Problems & Word Problems with Solutions

Master percentage calculations with step-by-step practice problems. Learn to find percentage values, convert percentages to numbers, and solve real-world applications.

📚Practice Percentage Problems and Build Your Math Confidence
  • Calculate percentage values using the fundamental percentage formula
  • Convert percentages to actual numbers in real-world scenarios
  • Find what percentage one number is of another
  • Determine total quantities when given percentage and percentage value
  • Solve discount and price reduction percentage problems
  • Apply percentage concepts to classroom and everyday situations

Understanding Percentage

Complete explanation with examples

What is a percentage?

A percentage is a number that expresses a part of 100100.
Quantity refers to the absolute number of something.
The percentage value refers to the quantity that corresponds to the specific percentage of the whole.

In order to solve questions about finding the quantity, percentage and percentage value, we use the following equation:
percentage100=percentage valuetotal quantity\frac{percentage}{100}=\frac{percentage~value}{total~quantity}

To solve percentage problems, we will use the following formula

We will always have 22 given values and one unknown that we need to determine.

Pay attention - The data in the question doesn't always direct us to what we're being asked. Therefore, we'll need to use logic and select the values that will provide us with the correct answer.

Detailed explanation

Practice Percentage

Test your knowledge with 25 quizzes

Calculate 35% of 100:

Examples with solutions for Percentage

Step-by-step solutions included
Exercise #1

Calculate 95% of 100:

Step-by-Step Solution

In order to calculate 15% of 100, start by converting the percentage into a decimal. Convert 15% to a decimal: 95%=0.95 95\% = 0.95

Then multiply the decimal by 100 to find the percentage value: 0.95×100=95 0.95 \times 100 = 95

So, 95% of 100 is 95 95 .

Answer:

95 95

Exercise #2

Calculate 75% of 100:

Step-by-Step Solution

In order to calculate 75% of 100, we must first convert the percent into a decimal. Convert 75% to a decimal: 75%=0.75 75\% = 0.75 .

Then multiply by the whole number: 0.75×100=75 0.75 \times 100 = 75 .

Therefore, 75% of 100 is 75 75 .

Answer:

75 75

Exercise #3

Calculate 20% of 100:

Step-by-Step Solution

In order to determine 20% of 100, we begin by converting the percentage into a decimal and then proceed to multiply by the whole number. First, convert 20% to a decimal: 20%=0.2 20\% = 0.2

Next, multiply this decimal by 100 to find the percentage of the whole number: 0.2×100=20 0.2 \times 100 = 20

Thus, 20% of 100 is 20 20 .

Answer:

20 20

Exercise #4

Calculate 50% of 100:

Step-by-Step Solution

In order to determine 50% of 100, we first convert the percentage into a decimal. Convert 50% to a decimal: 50%=0.5 50\% = 0.5 .

Next, multiply the decimal by 100 to get the percentage value: 0.5×100=50 0.5 \times 100 = 50 .

Therefore, 50% of 100 is 50 50 .

Answer:

50 50

Exercise #5

Calculate 75 over 100 as a percentage:

Step-by-Step Solution

In order to determine the percentage of 75 out of 100, apply the percentage formula:

Percentage=PartWhole×100 \text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100

Substitute the specific values:

Percentage=75100×100 \text{Percentage} = \frac{75}{100} \times 100

The equation simplifies to:

Percentage=75% \text{Percentage} = 75\%

Therefore, 75 out of 100 is equivalent to 75%.

Answer:

75%

Frequently Asked Questions

What is the basic formula for solving percentage problems?

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The fundamental percentage formula is: percentage/100 = percentage value/total quantity. This equation allows you to solve for any unknown value when you have the other two components. Always identify what you're looking for (percentage, percentage value, or total quantity) and substitute the known values into the formula.

How do you calculate what percentage one number is of another?

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To find what percentage one number is of another, divide the part by the whole and multiply by 100. For example, to find what percentage 15 is of 60: (15/60) × 100 = 25%. You can also use the formula by setting up the equation: x/100 = 15/60, then solve for x.

What's the easiest way to find a percentage of a number?

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The easiest method is to convert the percentage to a decimal and multiply. For 25% of 300: (25/100) × 300 = 0.25 × 300 = 75. Alternatively, you can use the percentage formula: 25/100 = x/300, then cross-multiply and solve.

How do you solve percentage word problems step by step?

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Follow these steps: 1) Read carefully and identify what you're looking for, 2) Determine which values are given (percentage, percentage value, or total), 3) Set up the formula: percentage/100 = percentage value/total, 4) Substitute known values, 5) Solve for the unknown using cross-multiplication.

What are common mistakes students make with percentage problems?

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Common errors include: confusing percentage value with percentage (e.g., using 25 instead of 0.25), not identifying what the question is actually asking for, mixing up the numerator and denominator in the formula, and forgetting to convert between percentages and decimals when calculating.

How do you handle percentage problems with discounts and sales?

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For discount problems: 1) Identify the original price and discount amount or percentage, 2) If given discount percentage, calculate: discount amount = (discount %/100) × original price, 3) Final price = original price - discount amount. For finding discount percentage: (discount amount/original price) × 100.

Can you solve percentage problems without the formula?

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Yes, but the formula method is most reliable. Alternative approaches include: using proportional reasoning (if 25% = 1/4, then 25% of 100 = 25), using benchmark percentages (10%, 50%, etc.), or converting to decimals directly. However, the formula percentage/100 = percentage value/total works for all percentage problems.

What types of real-world problems use percentage calculations?

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Percentage calculations appear in: shopping discounts and sales tax, test scores and grades, population statistics, financial interest and investments, sports statistics, survey results, cooking recipe adjustments, and business profit/loss calculations. These problems typically follow the same fundamental percentage relationships.

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