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

Comprehensive practice on fractions of a whole number: solving various question types 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 Question Bank

Question 1: What is 13 of 18?

Question 2: Find 35 of 25.

Question 3: A pizza has 12 slices. If Tom eats 14 of the pizza, how many slices does he eat?

Question 4: In a class of 24 students, 23 of the students are girls. How many girls are in the class?

Question 5: What is 46 of 18?

Solution: Exercises 1 to 3
1 Basic Fraction Questions
Exercise 1
What is 13 of 18?
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 (18 ÷ 3 = 6)
  2. Multiply the result by the numerator (6 × 1 = 6)
  3. The answer is the fraction of the whole number
Step 1: Divide by denominator: 18 ÷ 3 = 6
Step 2: Multiply by numerator: 6 × 1 = 6
Step 1: Divide by denominator

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

Step 2: Multiply by numerator

6 × 1 = 6 (we want 1 part out of 3)

13 of 18 = 6
Final answer:

13 of 18 is 6

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 18 items is 6 items

2 Intermediate Fraction Questions
Exercise 2
Find 35 of 25.
Definition:

Finding three-fifths: Dividing the number into 5 equal parts and taking 3 of those parts.

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Step 1: Divide by denominator: 25 ÷ 5 = 5
Step 2: Multiply by numerator: 5 × 3 = 15
Step 1: Divide by denominator

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

Step 2: Multiply by numerator

5 × 3 = 15 (we want 3 parts out of 5)

Step 3: Verify the result

If 35 of 25 is 15, then 25 of 25 should be 10, and 15 + 10 = 25 ✓

35 of 25 = 15
Final answer:

35 of 25 is 15

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 Word Problem Questions
Exercise 3
A pizza has 12 slices. If Tom eats 14 of the pizza, how many slices does he eat?
Definition:

Word problem with fractions: Applying fraction calculations to solve real-world scenarios.

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Step 1: Divide by denominator: 12 ÷ 4 = 3
Step 2: Multiply by numerator: 3 × 1 = 3
Step 1: Identify the problem

Total slices = 12, Tom eats 14 of the pizza

Step 2: Divide by denominator

12 ÷ 4 = 3 (one-fourth of 12 is 3)

Step 3: Multiply by numerator

3 × 1 = 3 (Tom eats 1 part out of 4)

Step 4: Answer the question

Tom eats 3 slices of pizza

14 of 12 = 3 slices
Final answer:

Tom eats 3 slices of pizza

Applied rules:

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

• Real-world context: Apply mathematical operations to solve practical problems

• Verification: 3 + 9 = 12, confirming the calculation

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 Population Problems
Exercise 4
In a class of 24 students, 23 of the students are girls. How many girls are in the class?
Definition:

Population fraction problems: Finding parts of a group using fractional relationships.

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Step 1: Divide by denominator: 24 ÷ 3 = 8
Step 2: Multiply by numerator: 8 × 2 = 16
Step 1: Identify the problem

24 students total, 23 are girls

Step 2: Divide by denominator

24 ÷ 3 = 8 (one-third of 24 is 8)

Step 3: Multiply by numerator

8 × 2 = 16 (two-thirds means 2 parts out of 3)

Step 4: Answer the question

There are 16 girls in the class

23 of 24 = 16 girls
Final answer:

There are 16 girls in the class

Applied rules:

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

• Group fraction problems: Apply to populations and collections

• Verification: 16 + 8 = 24, confirming the calculation

5 Complex Fraction Questions
Exercise 5
What is 46 of 18?
Definition:

Complex fraction problems: Working with fractions that may need simplification.

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Step 1: Divide by denominator: 18 ÷ 6 = 3
Step 2: Multiply by numerator: 3 × 4 = 12
Step 1: Divide by denominator

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

Step 2: Multiply by numerator

3 × 4 = 12 (we want 4 parts out of 6)

Step 3: Simplify the fraction (optional)

46 = 23, so we could also calculate 23 of 18 = (18 ÷ 3) × 2 = 12

Step 4: Verify the result

Four-sixths of 18 is the same as two-thirds of 18, which equals 12 ✓

46 of 18 = 12
Final answer:

46 of 18 is 12

Applied rules:

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

• Equivalent fractions: 46 = 23

• Verification: Different approaches yield the same result

Questions & Answers

Question: What if the fraction is bigger than the whole number? Like 54 of 8?

Answer: Great question! When the fraction is bigger than 1 (numerator > denominator), the result will be larger than the original number. Let's calculate 54 of 8:

  • Divide by denominator: 8 ÷ 4 = 2
  • Multiply by numerator: 2 × 5 = 10

So 54 of 8 = 10, which is indeed larger than 8. This makes sense because 54 = 114, which is more than one whole!

Question: My child sometimes gets confused when the denominator doesn't divide evenly into the whole number. How should we handle that?

Answer: At the 3rd grade level, focus on problems where the division results in a whole number. For example, use 13 of 12 rather than 13 of 10.

If you encounter a situation where the division doesn't result in a whole number, you can explain that some fractions of numbers result in parts, but for now, stick to problems that divide evenly. The key is ensuring students master the basic concept before moving to more complex scenarios.

Look for whole numbers that are multiples of the denominator to ensure clean division results.

Question: How can I quickly check if I did the fraction problem correctly?

Answer: Here are quick checking strategies:

  • Size check: Your answer should usually be smaller than the original number (unless the fraction is greater than 1)
  • Reasonableness: Does the answer make sense in the context of the problem?
  • Reversibility: If 23 of 15 is 10, then 10 should represent 2 out of 3 equal parts of 15
  • Estimation: Round numbers to check if your answer is close to what you'd expect

Always ask yourself: "Does this answer seem reasonable?" before moving on.