Solved Exercises on Fractions of a Whole Number Worksheets in Grade 3

Comprehensive practice worksheets on fractions of whole numbers: solving various problems with detailed solutions and visual aids.

Complete Summary: Fractions of a Whole Number

Definitions

Fraction of a Whole Number: A calculation that finds a part of a whole number. For example, 14 of 12 means finding one-fourth of 12.

Whole Number: Any positive integer including zero (0, 1, 2, 3, 4...).

Fraction: A number that represents a part of a whole, with a numerator and denominator.

Multiplicative Thinking: Understanding that finding a fraction of a number involves multiplication and division.

Division Concept: Finding ab of n means dividing n by b and multiplying by a.

Core Rules and Laws

Fraction of a Number Rule: ab of n = (n ÷ b) × a

Order of Operations: Divide first, then multiply (following the fraction interpretation).

Equivalent Expressions: ab of n = n × ab

Whole Equals One: nn of any number equals the whole number.

Nothing Equals Zero: 0n of any number equals 0.

Step-by-Step Method

  1. Identify the fraction and whole number: Find what fraction you need and what number you're finding it of
  2. Divide the whole number by the denominator: This finds the value of one part
  3. Multiply by the numerator: This finds the value of the required number of parts
  4. Check your answer: Verify it makes sense in the context

Examples (Simple to Advanced)

Simple: 12 of 10 = (10 ÷ 2) × 1 = 5

Intermediate: 23 of 12 = (12 ÷ 3) × 2 = 8

Advanced: 34 of 20 = (20 ÷ 4) × 3 = 15

Tips, Tricks, and Common Pitfalls

Tips: Always divide by the denominator first, then multiply by the numerator.

Tricks: Use visual models like arrays or groups to understand the concept.

Common Pitfalls: Confusing the order of operations, multiplying first instead of dividing.

Key Notes for Memorization

Memory Aid: "Divide by bottom, multiply by top" - denominator first, then numerator.

Visual Memory: Think of dividing objects into groups, then taking required groups.

Quick Check: The answer should be smaller than the original number (unless fraction > 1).

Practice Worksheet: Fractions of Whole Numbers

Exercise 1: Find 13 of 15

Answer: (15 ÷ 3) × 1 = 5 × 1 = 5

Exercise 2: What is 25 of 20?

Answer: (20 ÷ 5) × 2 = 4 × 2 = 8

Exercise 3: Find 34 of 16

Answer: (16 ÷ 4) × 3 = 4 × 3 = 12

Exercise 4: What is 16 of 18?

Answer: (18 ÷ 6) × 1 = 3 × 1 = 3

Exercise 5: Find 45 of 25

Answer: (25 ÷ 5) × 4 = 5 × 4 = 20

Solution: Exercises 1 to 3
1 Basic Fraction Calculations
Exercise 1
Find 13 of 15
Definition:

Finding one-third: Dividing the number by 3 to find one part out of three equal parts.

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Method for finding fractions of whole numbers:
  1. Divide the whole number by the denominator (15 ÷ 3 = 5)
  2. Multiply the result by the numerator (5 × 1 = 5)
  3. The answer is the fraction of the whole number
Step 1: Divide by denominator: 15 ÷ 3 = 5
Step 2: Multiply by numerator: 5 × 1 = 5
Step 1: Divide by denominator

15 ÷ 3 = 5 (this gives us the value of one part)

Step 2: Multiply by numerator

5 × 1 = 5 (we want 1 part out of 3)

13 of 15 = 5
Final answer:

13 of 15 is 5

Applied rules:

• Fraction of a number rule: ab of n = (n ÷ b) × a

• Division first: Always divide by denominator before multiplying

• Visual confirmation: One-third of 15 items is 5 items

2 Intermediate Fraction Calculations
Exercise 2
What is 25 of 20?
Definition:

Finding two-fifths: Dividing the number into 5 equal parts and taking 2 of those parts.

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Step 1: Divide by denominator: 20 ÷ 5 = 4
Step 2: Multiply by numerator: 4 × 2 = 8
Step 1: Divide by denominator

20 ÷ 5 = 4 (this gives us the value of one part)

Step 2: Multiply by numerator

4 × 2 = 8 (we want 2 parts out of 5)

Step 3: Verify the result

If 25 of 20 is 8, then 35 of 20 should be 12, and 8 + 12 = 20 ✓

25 of 20 = 8
Final answer:

25 of 20 is 8

Applied rules:

• Fraction of a number rule: ab of n = (n ÷ b) × a

• Division first: Always divide by denominator before multiplying

• Verification: Check that parts add up to the whole

3 Advanced Fraction Calculations
Exercise 3
Find 34 of 16
Definition:

Finding three-fourths: Dividing the number into 4 equal parts and taking 3 of those parts.

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Step 1: Divide by denominator: 16 ÷ 4 = 4
Step 2: Multiply by numerator: 4 × 3 = 12
Step 1: Divide by denominator

16 ÷ 4 = 4 (this gives us the value of one part)

Step 2: Multiply by numerator

4 × 3 = 12 (we want 3 parts out of 4)

Step 3: Verify the result

One-fourth of 16 is 4, so three-fourths is 3 × 4 = 12 ✓

34 of 16 = 12
Final answer:

34 of 16 is 12

Applied rules:

• Fraction of a number rule: ab of n = (n ÷ b) × a

• Division first: Always divide by denominator before multiplying

• Visual confirmation: Pattern shows 3 out of every 4 items are selected

Rules and methods, laws,...
ab of n = (n ÷ b) × a
Fraction of a Whole Number
Rule 1
12 of n = n ÷ 2
Half of a number
Rule 2
13 of n = n ÷ 3
Third of a number
Rule 3
nn of m = m
All of a number
Key definitions:

Numerator: The top number in a fraction (how many parts taken)

Denominator: The bottom number in a fraction (total equal parts)

Whole number: Any positive integer including zero

Complete methodology:
  1. Identify the fraction and number: Determine what fraction and what number
  2. Divide by denominator: This finds the value of one equal part
  3. Multiply by numerator: This finds the value of required parts
  4. Verify the answer: Check if it makes sense in context
Tip 1: Always divide by the denominator first, then multiply by the numerator.
Tip 2: Use visual models to understand the concept before calculating.
Tip 3: The answer should be smaller than the original number (unless fraction > 1).
Tip 4: Check your answer by seeing if the parts add up to the whole.
Common errors: Multiplying before dividing, confusing numerator and denominator roles.
Key insights: Fractions of numbers connect multiplication and division concepts.
Formulas to know by heart:

• Fraction of a number: ab of n = (n ÷ b) × a

• Half of a number: 12 of n = n ÷ 2

• Third of a number: 13 of n = n ÷ 3

Solution: Exercises 4 to 5
4 Fraction Applications
Exercise 4
What is 16 of 18?
Definition:

Finding one-sixth: Dividing the number by 6 to find one part out of six equal parts.

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Step 1: Divide by denominator: 18 ÷ 6 = 3
Step 2: Multiply by numerator: 3 × 1 = 3
Step 1: Divide by denominator

18 ÷ 6 = 3 (this gives us the value of one part)

Step 2: Multiply by numerator

3 × 1 = 3 (we want 1 part out of 6)

Step 3: Verify the result

One-sixth of 18 is 3, so six-sixths would be 6 × 3 = 18 ✓

16 of 18 = 3
Final answer:

16 of 18 is 3

Applied rules:

• Fraction of a number rule: ab of n = (n ÷ b) × a

• Division first: Always divide by denominator before multiplying

• Visual confirmation: One-sixth of 18 items is 3 items

5 Complex Fraction Calculations
Exercise 5
Find 45 of 25
Definition:

Finding four-fifths: Dividing the number into 5 equal parts and taking 4 of those parts.

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Step 1: Divide by denominator: 25 ÷ 5 = 5
Step 2: Multiply by numerator: 5 × 4 = 20
Step 1: Divide by denominator

25 ÷ 5 = 5 (this gives us the value of one part)

Step 2: Multiply by numerator

5 × 4 = 20 (we want 4 parts out of 5)

Step 3: Verify the result

Four-fifths of 25 is the same as one-fifth of 25 multiplied by 4: 5 × 4 = 20 ✓

45 of 25 = 20
Final answer:

45 of 25 is 20

Applied rules:

• Fraction of a number rule: ab of n = (n ÷ b) × a

• Division first: Always divide by denominator before multiplying

• Verification: Different approaches yield the same result

Questions & Answers

Question: Why do I divide first and then multiply when finding fractions of numbers? Can't I multiply first?

Answer: Great question! You divide first because the fraction tells you to split the number into equal parts first. Here's why:

  • Division finds the size of each part: If you want 23 of 15, first find how big one-third is: 15 ÷ 3 = 5
  • Multiplication finds the total of selected parts: Then take 2 of those parts: 5 × 2 = 10
  • Order matters: 15 ÷ 3 × 2 = 10, but 15 × 2 ÷ 3 = 10 too, but the thinking process is clearer when you divide first

Think of it as: "First, figure out how big each piece is, then count how many pieces you want."

Question: My child is having trouble with the worksheets. What strategies can help them practice?

Answer: Here are effective strategies for fraction practice:

  • Use manipulatives: Counters, blocks, or drawings to make abstract concepts concrete
  • Start simple: Begin with halves and quarters before moving to other fractions
  • Practice daily: Short, regular sessions work better than long ones
  • Connect to real life: Use examples like sharing food or dividing toys

Focus on understanding the concept before rushing to memorize procedures. The visual representation helps build strong foundations.

Question: How do I check if my answer is right when finding fractions of numbers?

Answer: Here are good ways to check your fraction answers:

  • Does it make sense?: Your answer should be smaller than the original number (unless the fraction is greater than 1)
  • Add the parts: If you found 25 of a number, the remaining 35 should add up to the original number
  • Reverse the operation: If 14 of 20 is 5, then 5 × 4 should equal 20
  • Estimate: Make sure your answer is reasonable compared to the original number

Always ask yourself: "Is this answer logical in the context of the problem?"