Grade 4 · Fractions & Decimals · MAT-04-FD-005
Add Fractions with Like Denominators
Represent and solve add fractions with like denominators problems using accurate mathematical models, notation, and reasoning.
Learning objectives
What you should be able to do
- Represent and solve add fractions with like denominators problems using accurate mathematical models, notation, and reasoning.
- Explain why a strategy for add 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
Add 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 add 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.
Add 1/5 + 2/5.
1/5 + 2/5 = 3/5Equal denominators keep the unit-fraction size fixed, so the numerators count how many of those parts are combined.
Add 2/6 + 4/6.
2/6 + 4/6 = 6/6Equal denominators keep the unit-fraction size fixed, so the numerators count how many of those parts are combined.
Add 3/7 + 2/7.
3/7 + 2/7 = 5/7Equal denominators keep the unit-fraction size fixed, so the numerators count how many of those parts are combined.
Add 4/8 + 4/8.
4/8 + 4/8 = 8/8Equal denominators keep the unit-fraction size fixed, so the numerators count how many of those parts are combined.
Add 1/9 + 2/9.
1/9 + 2/9 = 3/9Equal denominators keep the unit-fraction size fixed, so the numerators count how many of those parts are combined.
Add 2/10 + 4/10.
2/10 + 4/10 = 6/10Equal denominators keep the unit-fraction size fixed, so the numerators count how many of those parts are combined.
Add 3/11 + 2/11.
3/11 + 2/11 = 5/11Equal denominators keep the unit-fraction size fixed, so the numerators count how many of those parts are combined.
Add 4/12 + 4/12.
4/12 + 4/12 = 8/12Equal denominators keep the unit-fraction size fixed, so the numerators count how many of those parts are combined.
Add 1/13 + 2/13.
1/13 + 2/13 = 3/13Equal denominators keep the unit-fraction size fixed, so the numerators count how many of those parts are combined.
Add 2/14 + 4/14.
2/14 + 4/14 = 6/14Equal denominators keep the unit-fraction size fixed, so the numerators count how many of those parts are combined.
Add 3/15 + 2/15.
3/15 + 2/15 = 5/15Equal denominators keep the unit-fraction size fixed, so the numerators count how many of those parts are combined.
Add 4/16 + 4/16.
4/16 + 4/16 = 8/16Equal denominators keep the unit-fraction size fixed, so the numerators count how many of those parts are combined.
Add 1/17 + 2/17.
1/17 + 2/17 = 3/17Equal denominators keep the unit-fraction size fixed, so the numerators count how many of those parts are combined.
Add 2/18 + 4/18.
2/18 + 4/18 = 6/18Equal denominators keep the unit-fraction size fixed, so the numerators count how many of those parts are combined.
Add 3/19 + 2/19.
3/19 + 2/19 = 5/19Equal denominators keep the unit-fraction size fixed, so the numerators count how many of those parts are combined.
Add 4/20 + 4/20.
4/20 + 4/20 = 8/20Equal denominators keep the unit-fraction size fixed, so the numerators count how many of those parts are combined.
Add 1/21 + 2/21.
1/21 + 2/21 = 3/21Equal denominators keep the unit-fraction size fixed, so the numerators count how many of those parts are combined.
Add 2/22 + 4/22.
2/22 + 4/22 = 6/22Equal denominators keep the unit-fraction size fixed, so the numerators count how many of those parts are combined.
Add 3/23 + 2/23.
3/23 + 2/23 = 5/23Equal denominators keep the unit-fraction size fixed, so the numerators count how many of those parts are combined.
Add 4/24 + 4/24.
4/24 + 4/24 = 8/24Equal denominators keep the unit-fraction size fixed, so the numerators count how many of those parts are combined.
Practice
Guided practice with hints
01Add 1/25 + 2/25.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 1/25 + 2/25 = 3/25
02Add 2/26 + 4/26.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 2/26 + 4/26 = 6/26
03Add 3/27 + 2/27.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 3/27 + 2/27 = 5/27
04Add 4/28 + 4/28.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 4/28 + 4/28 = 8/28
05Add 1/29 + 2/29.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 1/29 + 2/29 = 3/29
06Add 2/30 + 4/30.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 2/30 + 4/30 = 6/30
Practice
Independent practice
01Add 3/31 + 2/31.
Answer: 3/31 + 2/31 = 5/31
02Add 4/32 + 4/32.
Answer: 4/32 + 4/32 = 8/32
03Add 1/33 + 2/33.
Answer: 1/33 + 2/33 = 3/33
04Add 2/34 + 4/34.
Answer: 2/34 + 4/34 = 6/34
05Add 3/35 + 2/35.
Answer: 3/35 + 2/35 = 5/35
06Add 4/36 + 4/36.
Answer: 4/36 + 4/36 = 8/36
07Add 1/37 + 2/37.
Answer: 1/37 + 2/37 = 3/37
08Add 2/38 + 4/38.
Answer: 2/38 + 4/38 = 6/38
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
Add 3/39 + 2/39.
3/39 + 2/39 = 5/39
Add 4/40 + 4/40.
4/40 + 4/40 = 8/40
Add 1/41 + 2/41.
1/41 + 2/41 = 3/41
Add 2/42 + 4/42.
2/42 + 4/42 = 6/42
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Grade 4 Math Strategy Sprint
Solve and explain add fractions with like denominators problems accurately, then check each result with a second method.
Practice
Mastery check
01Add 3/43 + 2/43.
Answer: 3/43 + 2/43 = 5/43
02Add 4/44 + 4/44.
Answer: 4/44 + 4/44 = 8/44
03Add 1/45 + 2/45.
Answer: 1/45 + 2/45 = 3/45
04Add 2/46 + 4/46.
Answer: 2/46 + 4/46 = 6/46
05Add 3/47 + 2/47.
Answer: 3/47 + 2/47 = 5/47
06Add 4/48 + 4/48.
Answer: 4/48 + 4/48 = 8/48
07Add 1/49 + 2/49.
Answer: 1/49 + 2/49 = 3/49
08Add 2/50 + 4/50.
Answer: 2/50 + 4/50 = 6/50
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.