Grade 3 · Number & Operations—Fractions · MAT-03-NF-008
Compare Fractions with the Same Numerator
Represent compare fractions with the same numerator with words, symbols, diagrams, or models appropriate to Grade 3.
Learning objectives
What you should be able to do
- Represent compare fractions with the same numerator with words, symbols, diagrams, or models appropriate to Grade 3.
- Solve problems involving compare fractions with the same numerator accurately and explain why the method works.
- Check results for reasonableness using a second representation, inverse relationship, benchmark, or property when appropriate.
Prerequisite check
Make sure the foundation is ready.
Checks conceptual readiness before new Grade 3 reasoning.
Checks whether prior skills are available for use, not only recalled by name.
Learn
Build the idea from meaning, not memorization.
Meaning of Compare Fractions with the Same Numerator
When fractions share a numerator, they contain the same number of parts, so the fraction with larger parts is greater.
A reliable reasoning strategy
Compare denominators by reasoning about unit-fraction size: fewer equal parts make larger pieces.
Representations that should agree
A number line makes the inverse relationship between denominator and unit-fraction size visible. A correct model, equation, verbal explanation, or diagram should preserve the same quantities and relationships.
How to check the result
Check whether the answer fits the quantities, units, and structure of the problem. Use a second representation or inverse relationship when available, and explain what would make an answer unreasonable.
Interactive math lab
Change it. See what stays true.
Equal-Share Lab
Keep the whole fixed and change how many equal shares it contains.
- build a model
- change one quantity
- predict before calculating
- explain why the result changes
Worked examples
Twenty different ways to see the concept work.
Compare 2/4 and 2/6.
2/4 > 2/6With equal numerators, the fraction with the smaller denominator has larger parts.
Compare 1/6 and 1/8.
1/6 > 1/8With equal numerators, the fraction with the smaller denominator has larger parts.
Compare 2/2 and 2/4.
2/2 > 2/4With equal numerators, the fraction with the smaller denominator has larger parts.
Compare 1/3 and 1/4.
1/3 > 1/4With equal numerators, the fraction with the smaller denominator has larger parts.
Compare 2/4 and 2/6.
2/4 > 2/6With equal numerators, the fraction with the smaller denominator has larger parts.
Compare 1/6 and 1/8.
1/6 > 1/8With equal numerators, the fraction with the smaller denominator has larger parts.
Compare 2/2 and 2/4.
2/2 > 2/4With equal numerators, the fraction with the smaller denominator has larger parts.
Compare 1/3 and 1/4.
1/3 > 1/4With equal numerators, the fraction with the smaller denominator has larger parts.
Compare 2/4 and 2/6.
2/4 > 2/6With equal numerators, the fraction with the smaller denominator has larger parts.
Compare 1/6 and 1/8.
1/6 > 1/8With equal numerators, the fraction with the smaller denominator has larger parts.
Compare 2/2 and 2/4.
2/2 > 2/4With equal numerators, the fraction with the smaller denominator has larger parts.
Compare 1/3 and 1/4.
1/3 > 1/4With equal numerators, the fraction with the smaller denominator has larger parts.
Compare 2/4 and 2/6.
2/4 > 2/6With equal numerators, the fraction with the smaller denominator has larger parts.
Compare 1/6 and 1/8.
1/6 > 1/8With equal numerators, the fraction with the smaller denominator has larger parts.
Compare 2/2 and 2/4.
2/2 > 2/4With equal numerators, the fraction with the smaller denominator has larger parts.
Compare 1/3 and 1/4.
1/3 > 1/4With equal numerators, the fraction with the smaller denominator has larger parts.
Compare 2/4 and 2/6.
2/4 > 2/6With equal numerators, the fraction with the smaller denominator has larger parts.
Compare 1/6 and 1/8.
1/6 > 1/8With equal numerators, the fraction with the smaller denominator has larger parts.
Compare 2/2 and 2/4.
2/2 > 2/4With equal numerators, the fraction with the smaller denominator has larger parts.
Compare 1/3 and 1/4.
1/3 > 1/4With equal numerators, the fraction with the smaller denominator has larger parts.
Practice
Guided practice with hints
01Compare 2/2 and 2/4.
Hint: Compare denominators by reasoning about unit-fraction size: fewer equal parts make larger pieces.
Answer: 2/2 > 2/4
02Compare 1/3 and 1/4.
Hint: Compare denominators by reasoning about unit-fraction size: fewer equal parts make larger pieces.
Answer: 1/3 > 1/4
03Compare 2/4 and 2/6.
Hint: Compare denominators by reasoning about unit-fraction size: fewer equal parts make larger pieces.
Answer: 2/4 > 2/6
04Compare 1/6 and 1/8.
Hint: Compare denominators by reasoning about unit-fraction size: fewer equal parts make larger pieces.
Answer: 1/6 > 1/8
05Compare 2/2 and 2/4.
Hint: Compare denominators by reasoning about unit-fraction size: fewer equal parts make larger pieces.
Answer: 2/2 > 2/4
06Compare 1/3 and 1/4.
Hint: Compare denominators by reasoning about unit-fraction size: fewer equal parts make larger pieces.
Answer: 1/3 > 1/4
Practice
Independent practice
01Compare 2/2 and 2/4.
Answer: 2/2 > 2/4
02Compare 1/3 and 1/4.
Answer: 1/3 > 1/4
03Compare 2/4 and 2/6.
Answer: 2/4 > 2/6
04Compare 1/6 and 1/8.
Answer: 1/6 > 1/8
05Compare 2/2 and 2/4.
Answer: 2/2 > 2/4
06Compare 1/3 and 1/4.
Answer: 1/3 > 1/4
07Compare 2/4 and 2/6.
Answer: 2/4 > 2/6
08Compare 1/6 and 1/8.
Answer: 1/6 > 1/8
Common mistakes
Learn to catch the error, not just the answer.
Remember that a larger denominator creates smaller equal parts when the whole is fixed.
Reconnect the answer to compare fractions with the same numerator and verify that the model, calculation, and label describe the same quantity.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Compare portions made from the same count of differently sized equal parts.
- Use compare fractions with the same numerator to interpret or solve a Grade 3 situation with quantities, diagrams, measurements, or data.
Challenge problems
Compare 2/2 and 2/4.
2/2 > 2/4
Compare 1/3 and 1/4.
1/3 > 1/4
Compare 2/4 and 2/6.
2/4 > 2/6
Compare 1/6 and 1/8.
1/6 > 1/8
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Compare Fractions with the Same Numerator Challenge
Solve and explain Grade 3 problems involving compare fractions with the same numerator without relying on answer guessing.
Practice
Mastery check
01Compare 2/2 and 2/4.
Answer: 2/2 > 2/4
02Compare 1/3 and 1/4.
Answer: 1/3 > 1/4
03Compare 2/4 and 2/6.
Answer: 2/4 > 2/6
04Compare 1/6 and 1/8.
Answer: 1/6 > 1/8
05Compare 2/2 and 2/4.
Answer: 2/2 > 2/4
06Compare 1/3 and 1/4.
Answer: 1/3 > 1/4
07Compare 2/4 and 2/6.
Answer: 2/4 > 2/6
08Compare 1/6 and 1/8.
Answer: 1/6 > 1/8
Terminology
Words to know
- common numerator
- The same numerator used by two fractions.
- unit-fraction size
- The size of one equal part of a whole.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Common Core State Standards for Mathematics — Grade 3, 3.NF.3.d
Primary standards alignment for Compare Fractions with the Same Numerator.2023 Mathematics Framework for California Public Schools
Instructional emphasis on reasoning, representations, problem solving, and equitable access.