Grade 3 · Number & Operations—Fractions · MAT-03-NF-007
Compare Fractions with the Same Denominator
Represent compare fractions with the same denominator 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 denominator with words, symbols, diagrams, or models appropriate to Grade 3.
- Solve problems involving compare fractions with the same denominator 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 Denominator
When fractions refer to the same whole and have the same denominator, they use equal-sized parts, so the fraction with more parts is greater.
A reliable reasoning strategy
Compare numerators only after confirming the denominators and wholes match.
Representations that should agree
Area models and number lines show that more copies of the same unit fraction produce a larger number. 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 2/6 and 3/6.
2/6 < 3/6With equal denominators, compare how many equal-sized parts are present.
Compare 3/8 and 5/8.
3/8 < 5/8With equal denominators, compare how many equal-sized parts are present.
Compare 1/4 and 1/4.
1/4 = 1/4With equal denominators, compare how many equal-sized parts are present.
Compare 5/6 and 4/6.
5/6 > 4/6With equal denominators, compare how many equal-sized parts are present.
Compare 6/8 and 4/8.
6/8 > 4/8With equal denominators, compare how many equal-sized parts are present.
Compare 1/4 and 1/4.
1/4 = 1/4With equal denominators, compare how many equal-sized parts are present.
Compare 3/6 and 5/6.
3/6 < 5/6With equal denominators, compare how many equal-sized parts are present.
Compare 2/8 and 3/8.
2/8 < 3/8With equal denominators, compare how many equal-sized parts are present.
Compare 1/4 and 1/4.
1/4 = 1/4With equal denominators, compare how many equal-sized parts are present.
Compare 1/6 and 1/6.
1/6 = 1/6With equal denominators, compare how many equal-sized parts are present.
Compare 5/8 and 2/8.
5/8 > 2/8With equal denominators, compare how many equal-sized parts are present.
Compare 1/4 and 1/4.
1/4 = 1/4With equal denominators, compare how many equal-sized parts are present.
Compare 4/6 and 2/6.
4/6 > 2/6With equal denominators, compare how many equal-sized parts are present.
Compare 1/8 and 1/8.
1/8 = 1/8With equal denominators, compare how many equal-sized parts are present.
Compare 1/4 and 1/4.
1/4 = 1/4With equal denominators, compare how many equal-sized parts are present.
Compare 2/6 and 3/6.
2/6 < 3/6With equal denominators, compare how many equal-sized parts are present.
Compare 4/8 and 7/8.
4/8 < 7/8With equal denominators, compare how many equal-sized parts are present.
Compare 1/4 and 1/4.
1/4 = 1/4With equal denominators, compare how many equal-sized parts are present.
Compare 5/6 and 4/6.
5/6 > 4/6With equal denominators, compare how many equal-sized parts are present.
Compare 7/8 and 6/8.
7/8 > 6/8With equal denominators, compare how many equal-sized parts are present.
Practice
Guided practice with hints
01Compare 2/6 and 3/6.
Hint: Compare numerators only after confirming the denominators and wholes match.
Answer: 2/6 < 3/6
02Compare 5/8 and 2/8.
Hint: Compare numerators only after confirming the denominators and wholes match.
Answer: 5/8 > 2/8
03Compare 1/4 and 1/4.
Hint: Compare numerators only after confirming the denominators and wholes match.
Answer: 1/4 = 1/4
04Compare 5/6 and 4/6.
Hint: Compare numerators only after confirming the denominators and wholes match.
Answer: 5/6 > 4/6
05Compare 1/8 and 1/8.
Hint: Compare numerators only after confirming the denominators and wholes match.
Answer: 1/8 = 1/8
06Compare 1/4 and 1/4.
Hint: Compare numerators only after confirming the denominators and wholes match.
Answer: 1/4 = 1/4
Practice
Independent practice
01Compare 1/4 and 1/4.
Answer: 1/4 = 1/4
02Compare 3/6 and 5/6.
Answer: 3/6 < 5/6
03Compare 5/8 and 2/8.
Answer: 5/8 > 2/8
04Compare 1/4 and 1/4.
Answer: 1/4 = 1/4
05Compare 1/6 and 1/6.
Answer: 1/6 = 1/6
06Compare 1/8 and 1/8.
Answer: 1/8 = 1/8
07Compare 1/4 and 1/4.
Answer: 1/4 = 1/4
08Compare 4/6 and 2/6.
Answer: 4/6 > 2/6
Common mistakes
Learn to catch the error, not just the answer.
First verify equal wholes and equal denominators; then compare the number of parts.
Reconnect the answer to compare fractions with the same denominator and verify that the model, calculation, and label describe the same quantity.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Compare equal-sized servings, distances, or completed portions.
- Use compare fractions with the same denominator to interpret or solve a Grade 3 situation with quantities, diagrams, measurements, or data.
Challenge problems
Compare 2/8 and 3/8.
2/8 < 3/8
Compare 1/4 and 1/4.
1/4 = 1/4
Compare 4/6 and 2/6.
4/6 > 2/6
Compare 5/8 and 2/8.
5/8 > 2/8
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Compare Fractions with the Same Denominator Challenge
Solve and explain Grade 3 problems involving compare fractions with the same denominator without relying on answer guessing.
Practice
Mastery check
01Compare 2/6 and 3/6.
Answer: 2/6 < 3/6
02Compare 2/8 and 3/8.
Answer: 2/8 < 3/8
03Compare 1/4 and 1/4.
Answer: 1/4 = 1/4
04Compare 5/6 and 4/6.
Answer: 5/6 > 4/6
05Compare 5/8 and 2/8.
Answer: 5/8 > 2/8
06Compare 1/4 and 1/4.
Answer: 1/4 = 1/4
07Compare 3/6 and 5/6.
Answer: 3/6 < 5/6
08Compare 1/8 and 1/8.
Answer: 1/8 = 1/8
Terminology
Words to know
- compare
- Decide whether one value is greater than, less than, or equal to another.
- common denominator
- The same denominator used by two fractions.
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 Denominator.2023 Mathematics Framework for California Public Schools
Instructional emphasis on reasoning, representations, problem solving, and equitable access.