Percentage Practice Problems - Calculate Parts of a Whole

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

📚What You'll Practice: Percentage Calculations and Real-World Applications
  • Convert fractions to percentages and solve part-of-whole problems
  • Calculate percentage discounts and price reductions in shopping scenarios
  • Apply the percentage formula: Part = Percentage × Whole
  • Convert percentages to decimals for multiplication calculations
  • Solve word problems involving percentage increases and decreases
  • Determine what percentage one number is of another number

Understanding Percentage

Complete explanation with examples

What are Percentages?

In order to recognise and calculate percentages, we need to understand two basic concepts:

  • How to determine a part of a whole without percentages
  • How to determine a part of a whole with percentages

When we are discussing percentages, one should always ask the question "percentage of what?", meaning, there must be some whole from which the percentage is calculated. The whole serves as a reference point for the percentages.

To solve percentage problems, we will use the following formula

Detailed explanation

Practice Percentage

Test your knowledge with 26 quizzes

Calculate 8% of 100:

Examples with solutions for Percentage

Step-by-step solutions included
Exercise #1

Calculate 30 over 100 as a percentage:

Step-by-Step Solution

In order to determine what percentage 30 is out of 100, you can use the following formula:

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

We begin by substituting the given values into the formula:

Percentage=30100×100 \text{Percentage} = \frac{30}{100} \times 100

We then proceed to simplify the expression:

Percentage=30% \text{Percentage} = 30\%

Therefore, 30 out of 100 is 30%.

Answer:

30%

Exercise #2

Calculate 3% of 100:

Step-by-Step Solution

To solve this problem, we'll proceed with the following steps:

  • Step 1: Identify the given information
    We are given a percentage of 3% and a whole number of 100.
  • Step 2: Use the percentage formula
    The formula to calculate the percentage of a whole number is given by:
    Percentage value=percentage100×whole number \text{Percentage value} = \frac{\text{percentage}}{100} \times \text{whole number}
  • Step 3: Substitute the values and calculate
    Substituting the given values into the formula, we have:
    3100×100=3 \frac{3}{100} \times 100 = 3

Therefore, the 3% of 100 is 3 3 .

Answer:

3

Video Solution
Exercise #3

Calculate 32 over 100 as a percentage:

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Identify the given fraction 32100 \frac{32}{100} .
  • Step 2: Recognize that the denominator of 100 aligns directly with the meaning of percentage.
  • Step 3: Conclude that when the fraction is Part100 \frac{\text{Part}}{100} , it equals Part% \text{Part}\% .

Now, let's work through each step:

Step 1: The problem gives us the fraction 32100 \frac{32}{100} .
Step 2: Since the denominator is 100, the fraction directly represents a percentage.
Step 3: This means that 32100 \frac{32}{100} is simply 32% 32\% .

Therefore, the solution to the problem is 32% 32\% .

Answer:

32%

Video Solution
Exercise #4

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

.

We begin by substituting in the known values:

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

.

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

Answer:

25%

Exercise #5

Calculate 40 over 100 as a percentage:

Step-by-Step Solution

In order to determine what percentage 40 is out of 100, we use the following formula:

Percentage=(PartWhole)×100 \text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100

We begin by substituting in the known values:

Percentage=(40100)×100 \text{Percentage} = \left( \frac{40}{100} \right) \times 100

We then proceed to solve the expression:

Percentage=0.4×100 \text{Percentage} = 0.4 \times 100

Percentage=40 \text{Percentage} = 40

Thus, 40 out of 100 is 40%.

Answer:

40%

Frequently Asked Questions

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%.

What's the easiest way to calculate percentage discounts?

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First, subtract the discount percentage from 100% to find what you'll pay. Then convert to decimal and multiply by the original price. For a 20% discount: pay 80%, so multiply the original price by 0.8.

How do you convert a percentage to a decimal for calculations?

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Divide the percentage by 100 or move the decimal point two places to the left. Examples: 25% = 0.25, 80% = 0.8, 5% = 0.05.

What does 'percentage of what' mean in word problems?

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This phrase helps identify the whole or reference point. The percentage is always calculated from this whole amount. Always ask 'percentage of what?' to find your starting value.

How do you solve percentage word problems step by step?

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Follow these steps: 1) Identify the whole amount, 2) Identify what percentage you need, 3) Convert percentage to decimal, 4) Multiply whole × decimal = part.

What's the difference between finding a part of a whole with and without percentages?

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Without percentages, you multiply a fraction by the whole (like 1/4 × 20). With percentages, you convert the percentage to a decimal first, then multiply (like 25% of 20 = 0.25 × 20).

How do you calculate the final price after a percentage discount?

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Method 1: Calculate discount amount and subtract from original price. Method 2: Find what percentage you pay (100% - discount%), convert to decimal, and multiply by original price.

Why do we multiply when finding a percentage of a number?

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Multiplication finds parts of wholes. When you want 25% of something, you're finding 25/100 of it, which requires multiplication. The percentage tells you what fraction of the whole you want.

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