Solved Exercises on Comparing Fractions with Same Denominator in Grade 3

Master comparing fractions with same denominator: identifying larger fractions, ordering fractions, and solving comparison word problems with visual representations through these 3 detailed exercises.

Solution: Exercises 1 to 3
1 Comparing Fractions with Same Denominator
Exercise 1
Compare 3/7 and 5/7. Which fraction is larger? Explain your reasoning using visual models.
Definition:

Comparing fractions with same denominator: When fractions have the same denominator, compare the numerators to determine which fraction is larger.

Comparison method:
  1. Check that denominators are the same
  2. Compare the numerators
  3. The fraction with the larger numerator is greater
  4. Draw visual models to confirm
Fractions
3/7 vs 5/7
Denominators
7 = 7
Numerators
3 vs 5
1
2
3
4
5
6
7
vs
1
2
3
4
5
6
7
Step 1: Verify denominators are the same

Both fractions have denominator 7, so we can compare numerators directly

Step 2: Compare numerators

3 < 5, so 3/7 < 5/7

Step 3: Verify with visual model

3 out of 7 parts is less than 5 out of 7 parts

Step 4: Write the comparison

3/7 < 5/7 (3/7 is less than 5/7)

Key Rule: When denominators are equal, compare numerators directly!
3/7 < 5/7
Final answer:

5/7 is larger than 3/7 because both fractions have the same denominator (7), and 5 > 3.

Applied rules:

• Same denominator rule: Compare numerators directly when denominators match

• Greater than: Larger numerator means larger fraction when denominators are equal

• Visual confirmation: Draw models to verify the comparison

2 Ordering Fractions with Same Denominator
Exercise 2
Order these fractions from smallest to largest: 2/6, 5/6, 1/6, 4/6
Explain your method for ordering.
Definition:

Ordering fractions with same denominator: Arranging fractions from smallest to largest by comparing their numerators when all denominators are equal.

2/6
5/6
1/6
4/6
Denominator
6
Numerators
1, 2, 4, 5
Order
1<2<4<5
1
2
3
4
5
6
1/6
1
2
3
4
5
6
2/6
1
2
3
4
5
6
4/6
1
2
3
4
5
6
5/6
Step 1: Verify all denominators are the same

All fractions have denominator 6, so we can compare numerators

Step 2: List the numerators

The numerators are: 2, 5, 1, 4

Step 3: Order the numerators from smallest to largest

1 < 2 < 4 < 5

Step 4: Write the fractions in the same order

1/6, 2/6, 4/6, 5/6

From smallest to largest: 1/6, 2/6, 4/6, 5/6
Final answer:

The fractions ordered from smallest to largest are: 1/6, 2/6, 4/6, 5/6

Applied rules:

• Same denominator ordering: Arrange numerators in ascending order

• Consistency: All fractions must have the same denominator

• Visual verification: Draw models to confirm the ordering

3 Word Problem Application
Exercise 3
Three friends are eating pizza. Tom ate 2/8 of the pizza, Sarah ate 5/8 of the pizza, and Jake ate 3/8 of the pizza. Who ate the most pizza? Who ate the least? Explain how you determined this.
Definition:

Real-world fraction comparison: Applying fraction comparison skills to solve practical problems involving quantities with the same denominator.

T
2
3
4
5
6
7
8
Tom: 2/8
S
S
S
S
S
6
7
8
Sarah: 5/8
J
J
J
4
5
6
7
8
Jake: 3/8
2/8
<
3/8
<
5/8
Step 1: Identify the fractions

Tom: 2/8, Sarah: 5/8, Jake: 3/8

Step 2: Check denominators

All fractions have denominator 8, so we can compare numerators

Step 3: Compare numerators

2 < 3 < 5

Step 4: Order the fractions

2/8 < 3/8 < 5/8

Final answer:

Sarah ate the most pizza (5/8), and Tom ate the least pizza (2/8).

Applied rules:

• Real-world application: Connect mathematical concepts to practical scenarios

• Same denominator comparison: Compare numerators directly

• Logical reasoning: Apply mathematical results to answer the question

Fraction Comparison Rules and Methods
a/c vs b/c → Compare a vs b
Same Denominator Rule
Same Denominator
3/5 vs 4/5
Compare numerators
Ordering
1/7, 3/7, 5/7
Arrange numerators
Visual Model
Shaded parts
More shading = larger
Key Rule: When denominators are the same, compare numerators directly.
Comparison Logic: Larger numerator means larger fraction when denominators match.
Tip 1: Always verify that denominators are the same before comparing numerators.
Tip 2: Draw visual models to confirm your comparisons.
Tip 3: Remember: More shaded parts = larger fraction when parts are equal.
Key Rules to Remember:

• Same denominator: Compare numerators directly

• Greater than: Larger numerator means larger fraction

• Ordering: Arrange numerators in desired order

• Visual verification: Draw models to confirm comparisons

If a < b, then a/c < b/c (when c > 0)
Comparison Formula
Fractions Denominator Numerators Comparison 2/7 vs 5/7 7 2 vs 5 2/7 < 5/7 3/8 vs 1/8 8 3 vs 1 3/8 > 1/8 4/9 vs 4/9 9 4 vs 4 4/9 = 4/9 6/10 vs 8/10 10 6 vs 8 6/10 < 8/10
Additional Practice
4 Mixed Comparison Practice
Exercise 4
Compare the following pairs of fractions:
a) 3/9 and 7/9
b) 5/12 and 2/12
c) 8/11 and 8/11
Definition:

Mixed practice: Combining different fraction comparisons to strengthen understanding of same denominator rules.

Part a: 3/9 vs 7/9

Same denominator (9), compare numerators: 3 < 7, so 3/9 < 7/9

Part b: 5/12 vs 2/12

Same denominator (12), compare numerators: 5 > 2, so 5/12 > 2/12

Part c: 8/11 vs 8/11

Same numerator and denominator, so 8/11 = 8/11

Final answers:

a) 3/9 < 7/9

b) 5/12 > 2/12

c) 8/11 = 8/11

Applied rules:

• Consistency: Apply the same method to all problems

• Same denominator: Compare numerators directly

• Equality: When both numerator and denominator are identical

5 Ordering Challenge
Exercise 5
Order these fractions from largest to smallest: 9/10, 3/10, 7/10, 1/10, 5/10
Then write them in ascending order.
Definition:

Descending and ascending order: Arranging fractions from greatest to least or least to greatest by comparing numerators.

Numerators
9, 3, 7, 1, 5
Descending
9, 7, 5, 3, 1
Ascending
1, 3, 5, 7, 9
Step 1: List all numerators

9, 3, 7, 1, 5

Step 2: Order from largest to smallest

9 > 7 > 5 > 3 > 1

Step 3: Write fractions in descending order

9/10, 7/10, 5/10, 3/10, 1/10

Step 4: Write fractions in ascending order

1/10, 3/10, 5/10, 7/10, 9/10

9/10
>
7/10
>
5/10
>
3/10
>
1/10
Final answer:

Descending order: 9/10, 7/10, 5/10, 3/10, 1/10

Ascending order: 1/10, 3/10, 5/10, 7/10, 9/10

Applied rules:

• Ordering: Arrange numerators in desired sequence

• Consistency: All fractions have same denominator

• Reversal: Ascending is opposite of descending

Comprehensive Summary: Comparing Fractions with Same Denominator
a/c vs b/c → Compare a vs b
Comparison Rule
Key Definitions:

Unit fractions with same denominator: Fractions that have the same denominator but different numerators.

Comparison: Determining which fraction is greater than, less than, or equal to another fraction.

Numerator: The top number in a fraction that represents how many parts are selected.

Denominator: The bottom number in a fraction that represents how many equal parts the whole is divided into.

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

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

Complete Methodology:
  1. Verify denominators: Ensure all fractions have the same denominator
  2. Compare numerators: Look at the top numbers of the fractions
  3. Determine relationship: Larger numerator means larger fraction
  4. Visual verification: Draw models to confirm comparisons
  5. Apply to problems: Use the rule in various contexts
Tip 1: When denominators are the same, focus only on the numerators.
Tip 2: Draw pictures to visualize which fraction is larger.
Tip 3: Remember: More parts shaded = larger fraction (when parts are equal).
Tip 4: The fraction with the larger numerator is always greater when denominators match.
Common errors: Comparing denominators instead of numerators, forgetting to verify same denominator.
Key insights: This rule provides a foundation for comparing all fractions.
Core Rules and Principles:

• Same denominator rule: Compare numerators directly when denominators match

• Greater than: Larger numerator means larger fraction

• Ordering principle: Arrange numerators in desired sequence

• Visual confirmation: Draw models to verify comparisons

• Consistency: All fractions must have the same denominator

Examples: 2/5 < 3/5, 7/8 > 5/8, 4/6 = 4/6
Comparison Examples
Memory aid: "When denominators are the same, compare the tops!"
Success check: If 3/7 < 5/7, then 3 < 5. ✓

Questions & Answers

Question: Why do I only look at the top number when the bottom numbers are the same?

Answer: Think of it like sharing pizza with friends:

Example with 8 slices:

  • If a pizza is cut into 8 equal slices, each slice is the same size
  • Getting 3 slices (3/8) gives you more pizza than getting 2 slices (2/8)
  • Since the slices are the same size, the number of slices matters

The rule: When the denominator is the same, all parts are equal size, so only the count (numerator) matters!

It's like having the same size cookie jar - the jar with more cookies has more!

Question: My child is having trouble remembering which number is the numerator and which is the denominator. How can I help?

Answer: Here are helpful memory tricks:

Numerator memory aids:

  • "NUmerator = NUmbler of parts you have"
  • Think "North" - it's on top
  • The numerator is "north" of the fraction line

Denominator memory aids:

  • "DENominator = DENotes the total number of parts"
  • Think "Down" - it's at the bottom
  • Like a "dungeon" - it sits down at the bottom

Visual strategy:

  • Write "Numerator = Number of parts you want" above the fraction line
  • Write "Denominator = Total number of parts" below the fraction line
  • Practice with lots of visual examples

Practice regularly with visual examples to reinforce the concept!

Question: What happens if the denominators are different? Can I still compare the numerators?

Answer: No, you cannot directly compare numerators when denominators are different!

Example: Comparing 2/3 and 3/4

  • 2/3 means 2 parts out of 3 equal parts
  • 3/4 means 3 parts out of 4 equal parts
  • The parts are different sizes (1/3 vs 1/4), so you can't just compare 2 and 3

What to do instead:

  • Find equivalent fractions with the same denominator
  • Or convert to decimals or percentages
  • Or draw visual models to compare

The rule "compare numerators" only works when denominators are the same!