Grade 4 · Fractions & Decimals · MAT-04-FD-006
Subtract Fractions with Like Denominators
Represent and solve subtract fractions with like denominators problems using accurate mathematical models, notation, and reasoning.
Learning objectives
What you should be able to do
- Represent and solve subtract fractions with like denominators problems using accurate mathematical models, notation, and reasoning.
- Explain why a strategy for subtract fractions with like denominators works and verify the result with an independent check.
Prerequisite check
Make sure the foundation is ready.
The new lesson builds directly on this prior concept, so the prerequisite should be usable rather than merely familiar.
Learn
Build the idea from meaning, not memorization.
Meaning and structure
Subtract Fractions with Like Denominators depends on treating fractions as numbers built from equal-sized units. The numerator counts those units and the denominator defines their size; operations are valid only when the units being combined are compatible.
Represent the idea
The Math Box uses fraction model as the primary representation. Translate the situation into numbers or geometry first, identify what stays fixed, then change one quantity at a time and observe which relationships remain invariant.
Reason, calculate, and verify
Estimate before calculating, then use the inverse operation or an equivalent representation to confirm the exact result.
Math Box · Interactive lesson
Touch the math. Change it. See what stays true.
Use the interactive model before and after the worked examples. Change the inputs, make a prediction, then use the model to test whether your reasoning holds.
Equal-Share Lab
Keep the whole fixed and change how many equal shares it contains.
- Build one example of subtract fractions with like denominators in the Math Box.
- Change one input and predict the effect before moving the control.
- Explain which mathematical relationship stayed invariant after the change.
Worked examples
Twenty different ways to see the concept work.
Subtract 4/5 − 2/5.
4/5 − 2/5 = 2/5Equal denominators mean equal-sized parts; subtract only the numerators.
Subtract 7/6 − 4/6.
7/6 − 4/6 = 3/6Equal denominators mean equal-sized parts; subtract only the numerators.
Subtract 6/7 − 2/7.
6/7 − 2/7 = 4/7Equal denominators mean equal-sized parts; subtract only the numerators.
Subtract 9/8 − 4/8.
9/8 − 4/8 = 5/8Equal denominators mean equal-sized parts; subtract only the numerators.
Subtract 4/9 − 2/9.
4/9 − 2/9 = 2/9Equal denominators mean equal-sized parts; subtract only the numerators.
Subtract 7/10 − 4/10.
7/10 − 4/10 = 3/10Equal denominators mean equal-sized parts; subtract only the numerators.
Subtract 6/11 − 2/11.
6/11 − 2/11 = 4/11Equal denominators mean equal-sized parts; subtract only the numerators.
Subtract 9/12 − 4/12.
9/12 − 4/12 = 5/12Equal denominators mean equal-sized parts; subtract only the numerators.
Subtract 4/13 − 2/13.
4/13 − 2/13 = 2/13Equal denominators mean equal-sized parts; subtract only the numerators.
Subtract 7/14 − 4/14.
7/14 − 4/14 = 3/14Equal denominators mean equal-sized parts; subtract only the numerators.
Subtract 6/15 − 2/15.
6/15 − 2/15 = 4/15Equal denominators mean equal-sized parts; subtract only the numerators.
Subtract 9/16 − 4/16.
9/16 − 4/16 = 5/16Equal denominators mean equal-sized parts; subtract only the numerators.
Subtract 4/17 − 2/17.
4/17 − 2/17 = 2/17Equal denominators mean equal-sized parts; subtract only the numerators.
Subtract 7/18 − 4/18.
7/18 − 4/18 = 3/18Equal denominators mean equal-sized parts; subtract only the numerators.
Subtract 6/19 − 2/19.
6/19 − 2/19 = 4/19Equal denominators mean equal-sized parts; subtract only the numerators.
Subtract 9/20 − 4/20.
9/20 − 4/20 = 5/20Equal denominators mean equal-sized parts; subtract only the numerators.
Subtract 4/21 − 2/21.
4/21 − 2/21 = 2/21Equal denominators mean equal-sized parts; subtract only the numerators.
Subtract 7/22 − 4/22.
7/22 − 4/22 = 3/22Equal denominators mean equal-sized parts; subtract only the numerators.
Subtract 6/23 − 2/23.
6/23 − 2/23 = 4/23Equal denominators mean equal-sized parts; subtract only the numerators.
Subtract 9/24 − 4/24.
9/24 − 4/24 = 5/24Equal denominators mean equal-sized parts; subtract only the numerators.
Practice
Guided practice with hints
01Subtract 4/25 − 2/25.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 4/25 − 2/25 = 2/25
02Subtract 7/26 − 4/26.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 7/26 − 4/26 = 3/26
03Subtract 6/27 − 2/27.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 6/27 − 2/27 = 4/27
04Subtract 9/28 − 4/28.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 9/28 − 4/28 = 5/28
05Subtract 4/29 − 2/29.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 4/29 − 2/29 = 2/29
06Subtract 7/30 − 4/30.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 7/30 − 4/30 = 3/30
Practice
Independent practice
01Subtract 6/31 − 2/31.
Answer: 6/31 − 2/31 = 4/31
02Subtract 9/32 − 4/32.
Answer: 9/32 − 4/32 = 5/32
03Subtract 4/33 − 2/33.
Answer: 4/33 − 2/33 = 2/33
04Subtract 7/34 − 4/34.
Answer: 7/34 − 4/34 = 3/34
05Subtract 6/35 − 2/35.
Answer: 6/35 − 2/35 = 4/35
06Subtract 9/36 − 4/36.
Answer: 9/36 − 4/36 = 5/36
07Subtract 4/37 − 2/37.
Answer: 4/37 − 2/37 = 2/37
08Subtract 7/38 − 4/38.
Answer: 7/38 − 4/38 = 3/38
Common mistakes
Learn to catch the error, not just the answer.
Track the size of the fractional unit first; fractions can be combined only when the units are compatible.
Compare complete fraction values with a model, benchmark, common denominator, or cross-product reasoning.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Scale recipes, measurements, money, and data while preserving the meaning of the unit.
- Compare quantities that are not whole numbers in science, construction, shopping, and measurement.
Challenge problems
Subtract 6/39 − 2/39.
6/39 − 2/39 = 4/39
Subtract 9/40 − 4/40.
9/40 − 4/40 = 5/40
Subtract 4/41 − 2/41.
4/41 − 2/41 = 2/41
Subtract 7/42 − 4/42.
7/42 − 4/42 = 3/42
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Grade 4 Math Strategy Sprint
Solve and explain subtract fractions with like denominators problems accurately, then check each result with a second method.
Practice
Mastery check
01Subtract 6/43 − 2/43.
Answer: 6/43 − 2/43 = 4/43
02Subtract 9/44 − 4/44.
Answer: 9/44 − 4/44 = 5/44
03Subtract 4/45 − 2/45.
Answer: 4/45 − 2/45 = 2/45
04Subtract 7/46 − 4/46.
Answer: 7/46 − 4/46 = 3/46
05Subtract 6/47 − 2/47.
Answer: 6/47 − 2/47 = 4/47
06Subtract 9/48 − 4/48.
Answer: 9/48 − 4/48 = 5/48
07Subtract 4/49 − 2/49.
Answer: 4/49 − 2/49 = 2/49
08Subtract 7/50 − 4/50.
Answer: 7/50 − 4/50 = 3/50
Terminology
Words to know
- numerator
- The number of selected equal parts or unit fractions.
- denominator
- The number of equal parts that make one whole.
- equivalent fractions
- Different fraction names for the same numerical value.
- benchmark
- A familiar reference value such as 0, 1/2, or 1 used for comparison.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Mathematics Framework (2023)
Grade-level instructional guidance, mathematical practices, and coherent progression.Common Core State Standards for Mathematics — Grades 4–5
Grade-level expectations for operations, number and fraction work, measurement, data, and geometry.Principles to Actions: Ensuring Mathematical Success for All
Evidence-based emphasis on reasoning, representations, discourse, and conceptual understanding.