Solved Exercises on Unit Fractions in Grade 3

Master unit fractions: identifying unit fractions, comparing unit fractions, and ordering unit fractions with visual representations through these 3 detailed exercises.

Solution: Exercises 1 to 3
1 Identifying Unit Fractions
Exercise 1
Which of these fractions are unit fractions? 1/4, 3/5, 1/8, 2/3, 1/10
Explain why each one is or isn't a unit fraction.
Definition:

Unit fraction: A fraction where the numerator is 1. It represents one part of a whole divided into equal parts.

Identification method:
  1. Look at the numerator (top number) of each fraction
  2. If the numerator is 1, it's a unit fraction
  3. If the numerator is anything other than 1, it's not a unit fraction
  4. Verify that the denominator is a positive integer
Numerator
Must be 1
Result
Unit Fraction
1
2
3
4
1/4 is a unit fraction
1
2
3
2/3 is NOT a unit fraction
Step 1: Check 1/4

Numerator is 1, so 1/4 is a unit fraction

Step 2: Check 3/5

Numerator is 3 (not 1), so 3/5 is not a unit fraction

Step 3: Check 1/8

Numerator is 1, so 1/8 is a unit fraction

Step 4: Check 2/3

Numerator is 2 (not 1), so 2/3 is not a unit fraction

Step 5: Check 1/10

Numerator is 1, so 1/10 is a unit fraction

Key Rule: A unit fraction has exactly 1 as its numerator!
Unit fractions: 1/4, 1/8, 1/10
Final answer:

The unit fractions are: 1/4, 1/8, and 1/10. These have numerator 1. The fractions 3/5 and 2/3 are not unit fractions because their numerators are not 1.

Applied rules:

• Unit fraction definition: Numerator must equal 1

• Identification: Check only the numerator, not the denominator

• Examples: 1/2, 1/3, 1/4, 1/5, etc. are all unit fractions

2 Comparing Unit Fractions
Exercise 2
Compare 1/3 and 1/5. Which is larger? Use visual models to explain your answer.
Definition:

Comparing unit fractions: When comparing unit fractions, the one with the smaller denominator is larger.

1/3
vs
1/5
1
2
3
1/3 (3 total parts)
1
2
3
4
5
1/5 (5 total parts)
Denominator
3
Larger Part
✓
Result
1/3 > 1/5
Step 1: Identify the fractions

We're comparing 1/3 and 1/5

Step 2: Compare denominators

1/3 has denominator 3, 1/5 has denominator 5

Step 3: Understand the relationship

Smaller denominator means larger parts

Step 4: Draw visual models

1/3 of a shape is larger than 1/5 of the same shape

Key Rule: For unit fractions, smaller denominator = larger fraction!
1/3 > 1/5
Final answer:

1/3 is larger than 1/5. When the numerators are the same (both 1), the fraction with the smaller denominator is larger.

Applied rules:

• Unit fraction comparison: Smaller denominator means larger fraction

• Visual verification: Draw models to confirm comparisons

• Part size relationship: More parts mean smaller individual parts

3 Ordering Unit Fractions
Exercise 3
Order these unit fractions from smallest to largest: 1/6, 1/4, 1/8, 1/3
Explain your reasoning.
Definition:

Ordering unit fractions: Arranging unit fractions from smallest to largest by comparing their denominators.

1/8
<
1/6
<
1/4
<
1/3
1
2
3
4
5
6
7
8
1/8 (smallest)
1
2
3
4
5
6
1/6
1
2
3
4
1/4
1
2
3
1/3 (largest)
Step 1: List the fractions

We have: 1/6, 1/4, 1/8, 1/3

Step 2: Compare denominators

Denominators are: 6, 4, 8, 3

Step 3: Order denominators from largest to smallest

8, 6, 4, 3 (largest to smallest)

Step 4: Order fractions from smallest to largest

Since larger denominator = smaller fraction: 1/8, 1/6, 1/4, 1/3

Key Rule: For unit fractions, order by denominators (reverse order)!
Final answer:

From smallest to largest: 1/8, 1/6, 1/4, 1/3

Applied rules:

• Ordering rule: For unit fractions, larger denominator = smaller fraction

• Reverse order: Order denominators in reverse for unit fractions

• Visual confirmation: Draw models to verify the ordering

Unit Fractions Rules and Methods
1/n where n > 0
Unit Fraction
Unit Fraction
1/4, 1/7, 1/10
Numerator = 1
Comparison
1/3 > 1/5
Smaller den = larger
Ordering
1/8 < 1/3
Reverse order
Key Rule: A unit fraction has exactly 1 as its numerator.
Comparison Logic: For unit fractions, smaller denominator means larger fraction.
Tip 1: Remember: Unit fractions always have 1 on top.
Tip 2: When comparing unit fractions, think: "more pieces = smaller pieces."
Tip 3: Draw pictures to visualize which fraction is larger.
Key Rules to Remember:

• Unit fraction definition: Numerator must equal 1

• Comparison rule: For unit fractions, smaller denominator = larger fraction

• Ordering rule: Arrange by denominators in reverse order

• Visual verification: Draw models to confirm comparisons

1/a > 1/b when a < b
Comparison Formula
Unit Fraction Denominator Relative Size Example Model 1/2 2 Largest Half of a whole 1/3 3 Large One third of a whole 1/4 4 Medium One quarter of a whole 1/8 8 Small One eighth of a whole
Additional Practice
4 Mixed Unit Fraction Practice
Exercise 4
Identify the unit fractions from this list: 1/7, 2/5, 1/9, 4/4, 1/12
Then order the unit fractions from largest to smallest.
Definition:

Mixed practice: Combining identification and ordering of unit fractions to strengthen understanding.

Step 1: Identify unit fractions

Unit fractions have numerator 1: 1/7, 1/9, 1/12 (not 2/5 or 4/4)

Step 2: Order by denominators (smallest to largest)

Denominators: 7, 9, 12 → 7 < 9 < 12

Step 3: Apply reverse ordering rule

For unit fractions: smallest denominator = largest fraction

Step 4: Write final order

From largest to smallest: 1/7, 1/9, 1/12

1/7
>
1/9
>
1/12
Final answers:

Unit fractions: 1/7, 1/9, 1/12

From largest to smallest: 1/7, 1/9, 1/12

Applied rules:

• Identification: Check that numerator equals 1

• Ordering: Reverse the order of denominators for unit fractions

• Verification: Confirm with visual models if needed

5 Problem Solving
Exercise 5
Sarah, John, and Mia each have a pizza of the same size. Sarah eats 1/3 of her pizza, John eats 1/6 of his pizza, and Mia eats 1/4 of her pizza. Who ate the largest piece? Who ate the smallest piece?
Definition:

Problem solving: Applying unit fraction concepts to real-world scenarios with visual representations.

1/3
vs
1/6
vs
1/4
Step 1: Identify the unit fractions

Sarah: 1/3, John: 1/6, Mia: 1/4

Step 2: Compare denominators

Denominators: 3, 6, 4

Step 3: Order denominators from smallest to largest

3 < 4 < 6

Step 4: Apply unit fraction rule

Smallest denominator = largest fraction: 1/3 > 1/4 > 1/6

Sarah: 1/3
>
Mia: 1/4
>
John: 1/6
Final answer:

Sarah ate the largest piece (1/3), and John ate the smallest piece (1/6).

Applied rules:

• Real-world application: Connect math to everyday situations

• Unit fraction comparison: Use the denominator rule

• Logical reasoning: Apply mathematical concepts to solve problems

Comprehensive Summary: Unit Fractions
1/n where n is a positive integer
Unit Fraction Formula
Key Definitions:

Unit fraction: A fraction with numerator 1 and a positive integer denominator (like 1/2, 1/3, 1/4).

Numerator: The top number in a fraction (for unit fractions, always 1).

Denominator: The bottom number in a fraction (for unit fractions, any positive integer).

Comparison: The process of determining which fraction is larger or smaller.

Ordering: Arranging fractions from smallest to largest or vice versa.

Visual model: A drawing or diagram that represents the fraction.

Complete Methodology:
  1. Identify unit fractions: Check if numerator equals 1
  2. Compare denominators: For unit fractions, smaller denominator = larger fraction
  3. Order fractions: Arrange by denominators in reverse order
  4. Visual verification: Draw models to confirm comparisons
  5. Apply to problems: Use unit fraction concepts in real-world scenarios
Tip 1: Remember: Unit fractions always have 1 as the numerator.
Tip 2: For unit fractions, think "more pieces = smaller individual pieces."
Tip 3: Draw pictures to visualize which fraction is larger.
Tip 4: The larger the denominator, the smaller the unit fraction.
Common errors: Forgetting that unit fractions must have numerator 1, confusing comparison rules, misordering fractions.
Key insights: Unit fractions provide a foundation for understanding all fractions and their relative sizes.
Core Rules and Principles:

• Definition rule: Unit fractions have numerator equal to 1

• Comparison principle: For unit fractions, smaller denominator = larger fraction

• Ordering principle: Arrange denominators in reverse order for unit fractions

• Visual confirmation: Draw models to verify comparisons

• Size relationship: As denominator increases, fraction value decreases

Examples: 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8, 1/9, 1/10...
Unit Fraction Examples
Memory aid: "Unit fractions have unity (1) on top!"
Success check: If 1/3 > 1/5, then 3 < 5 (denominator relationship). ✓

Questions & Answers

Question: Why is 1/3 bigger than 1/4? Doesn't 4 seem like a bigger number than 3?

Answer: This is a very common question! Think of it this way:

Using a pizza example:

  • 1/3 means you take 1 slice from a pizza cut into 3 equal pieces
  • 1/4 means you take 1 slice from a pizza cut into 4 equal pieces
  • The 1/3 slice is bigger because the pizza was cut into fewer pieces

The rule: For unit fractions, a smaller denominator means larger pieces.

So 1/3 > 1/4 because 3 < 4. The fewer pieces you divide something into, the bigger each piece is!

Question: My child is struggling with the concept of unit fractions. How can I help them understand this better?

Answer: Here are effective ways to teach unit fractions:

Use concrete examples:

  • Use food: Cut an apple into halves, thirds, quarters
  • Take 1 piece out of each - that's your unit fraction
  • Compare: 1 slice of 2 vs 1 slice of 4

Visual representations:

  • Draw circles divided into equal parts
  • Shade just 1 part in each circle
  • Compare the sizes of the shaded parts

Hands-on activities:

  • Use paper folding to create unit fractions
  • Play with fraction tiles or manipulatives
  • Practice with real objects like chocolate bars

Focus on the key idea: Unit fractions always have 1 as the top number!

Question: What about fractions like 2/3 or 3/4? Are these unit fractions too?

Answer: No, 2/3 and 3/4 are not unit fractions!

Unit fraction definition:

  • A unit fraction MUST have numerator 1
  • Examples of unit fractions: 1/2, 1/3, 1/4, 1/5, etc.
  • 2/3 has numerator 2 (not 1), so it's not a unit fraction
  • 3/4 has numerator 3 (not 1), so it's not a unit fraction

What they are called:

  • 2/3 and 3/4 are called "proper fractions" (numerator smaller than denominator)
  • Unit fractions are a special type of proper fraction with numerator = 1

The "unit" in unit fraction means the numerator is exactly one unit!