Solved Exercises on One Step Percentage Word Problems in Grade 3

Master one step percentage word problems: finding parts of whole, calculating percentages, and solving real-world scenarios through these 10 detailed exercises.

Solution: Exercises 1 to 3
1 Finding part of a whole
Exercise 1
What is 25% of 80?
Definition:

Percentage of a number: To find X% of Y, multiply Y by X/100

Solution method:
  1. Convert percentage to decimal: divide by 100
  2. Multiply the decimal by the whole number
  3. Simplify the result
Problem
25% of 80
Convert
0.25 × 80
Result
20
Step 1: Convert percentage to decimal

25% = 25 ÷ 100 = 0.25

Step 2: Multiply decimal by whole number

0.25 × 80 = 20

Step 3: State the final answer

25% of 80 is 20

25% of 80 = 20
Final answer:

25% of 80 = 20

Applied rules:

• Percentage conversion: Divide percentage by 100 to get decimal

• Multiplication: Multiply decimal by the whole amount

• Simplification: Calculate the final value

2 Finding percentage
Exercise 2
What percent of 50 is 10?
Definition:

Finding percentage: (Part ÷ Whole) × 100

Problem
?% of 50 = 10
Formula
(10 ÷ 50) × 100
Result
20%
Step 1: Set up the ratio

We want to find what percent of 50 equals 10

This means: (10 ÷ 50) × 100

Step 2: Calculate the division

10 ÷ 50 = 0.2

Step 3: Convert to percentage

0.2 × 100 = 20%

20% of 50 = 10
Final answer:

20% of 50 = 10

Applied rules:

• Percentage formula: (Part ÷ Whole) × 100

• Division: Calculate the ratio of part to whole

• Conversion: Multiply by 100 to get percentage

3 Real world problem
Exercise 3
A store has 40 apples. If 30% of the apples are red, how many red apples are there?
Definition:

Real world percentage: Finding a percentage of a total quantity

Problem
30% of 40
Convert
0.30 × 40
Result
12
Step 1: Identify what we're looking for

Find 30% of 40 apples

Step 2: Convert percentage to decimal

30% = 30 ÷ 100 = 0.30

Step 3: Multiply decimal by total

0.30 × 40 = 12

Step 4: State the answer in context

There are 12 red apples

30% of 40 = 12 red apples
Final answer:

There are 12 red apples

Applied rules:

• Contextualization: Understand what the percentage represents

• Conversion: Change percentage to decimal form

• Application: Multiply decimal by the total amount

Solution: Exercises 4 to 5
4 Finding percentage of a group
Exercise 4
In a class of 25 students, 5 students wear glasses. What percent of the class wears glasses?
Definition:

Percentage of a group: (Number in category ÷ Total number) × 100

Problem
(5 ÷ 25) × 100
Calculate
0.2 × 100
Result
20%
Step 1: Identify the part and whole

Part = 5 students with glasses

Whole = 25 total students

Step 2: Set up the fraction

5 ÷ 25 = 0.2

Step 3: Convert to percentage

0.2 × 100 = 20%

Step 4: State the answer

20% of the class wears glasses

(5 ÷ 25) × 100 = 20%
Final answer:

20% of the class wears glasses

Applied rules:

• Part-whole relationship: Identify the numerator and denominator

• Decimal conversion: Divide to get decimal form

• Percentage conversion: Multiply by 100

5 Finding missing value
Exercise 5
If 40% of a number is 20, what is the number?
Definition:

Finding the whole: If X% of a number is Y, then the number = (Y ÷ X%) × 100

Problem
40% of ? = 20
Set equation
0.40 × ? = 20
Solve
? = 20 ÷ 0.40
Result
50
Step 1: Set up the equation

Let the unknown number be N

40% of N = 20

Step 2: Convert percentage to decimal

40% = 0.40

Step 3: Solve for N

0.40 × N = 20

N = 20 ÷ 0.40

N = 50

Step 4: Verify the answer

40% of 50 = 0.40 × 50 = 20 ✓

The number is 50
Final answer:

The number is 50

Applied rules:

• Equation setup: Represent the unknown with a variable

• Algebraic manipulation: Isolate the variable

• Verification: Check answer by substituting back

Rules and methods, laws,...
X% of Y = (X ÷ 100) × Y
Finding Part of Whole
Formula 1
Part = (Percent ÷ 100) × Whole
Finding a part
Formula 2
Percent = (Part ÷ Whole) × 100
Finding percentage
Formula 3
Whole = (Part ÷ Percent) × 100
Finding the whole
Key Concept: Percentage Meaning

Percentage means "per hundred" - so 25% means 25 out of every 100

Common Percentages
50%
Half
25%
Quarter
10%
Tenth
1%
Hundredth
1
Identify what is being asked: part, percent, or whole
2
Choose the correct formula based on what's known
3
Convert percentage to decimal by dividing by 100
4
Perform the calculation and state the answer
📊
50% = ½
📋
25% = ¼
🎯
10% = ¹⁄₁₀
Complete Guide to One Step Percentage Problems
X% of Y = (X ÷ 100) × Y
Basic Formula
Key definitions:

Percentage: A number expressed as a fraction of 100

Part: The portion of the whole that the percentage represents

Whole: The total amount from which the percentage is taken

Complete methodology:
  1. Read the problem carefully: Identify what is given and what is asked
  2. Determine the type: Are you finding the part, the percent, or the whole?
  3. Select the formula: Use the appropriate formula for the problem type
  4. Calculate: Perform the arithmetic operations
  5. Check: Verify the answer makes sense in the context
Tip 1: Remember that "of" usually means multiplication in percentage problems.
Tip 2: To convert percentage to decimal, move decimal point two places left.
Tip 3: Check if your answer is reasonable by estimating.
Tip 4: Practice converting between percentages, decimals, and fractions.
Common errors: Forgetting to convert percentage to decimal, misidentifying part vs whole, calculation mistakes.
Exam preparation: Practice all three types of problems, memorize formulas, work on mental math.
Formulas to know by heart:

• Finding part: Part = (Percent ÷ 100) × Whole

• Finding percent: Percent = (Part ÷ Whole) × 100

• Finding whole: Whole = (Part ÷ Percent) × 100

Visual Percentage Guide

50%
Half
50%
½ = 50%
25%
Quarter
25%
¼ = 25%
10%
Tenth
10%
¹⁄₁₀ = 10%

Questions & Answers

Question: I don't understand when to multiply by the decimal and when to divide by the decimal in percentage problems. Can you explain the difference?

Answer: Great question! It depends on what you're trying to find:

  • To find a part of a whole (like 25% of 80), multiply: 0.25 × 80 = 20
  • To find the whole when you know the part and percentage (like if 25% of what number is 20), divide: 20 ÷ 0.25 = 80
  • To find the percentage (like what percent of 80 is 20), divide and multiply: (20 ÷ 80) × 100 = 25%

Think of it this way: when you're looking for a piece of something, you multiply. When you're trying to find the original whole, you divide.

Question: When I see "what percent of" in a problem, how do I know which number goes where in the calculation?

Answer: The key is to identify the part and the whole:

  • In "what percent of 50 is 10?", the word "of" tells us that 50 is the whole amount
  • The number after "is" is the part (10 in this case)
  • So the calculation is: (part ÷ whole) × 100 = (10 ÷ 50) × 100 = 20%

Remember the pattern: "What percent of [whole] is [part]?" Then use: (part ÷ whole) × 100

Question: How can I check if my percentage answer is correct? Sometimes I'm not sure about my answer.

Answer: There are several ways to verify your percentage calculations:

  • Estimation: Does your answer make sense? 25% of 80 should be less than half of 80 (which is 40)
  • Reverse calculation: If you found 25% of 80 = 20, check: 20 ÷ 80 = 0.25 = 25%
  • Use known percentages: If you calculated 50% of a number, it should equal half of that number

Always ask yourself: "Is this answer reasonable compared to the original numbers?"