Grade 4 · Fractions & Decimals · MAT-04-FD-007
Add and Subtract Mixed Numbers with Like Denominators
Represent and solve add and subtract mixed numbers with like denominators problems using accurate mathematical models, notation, and reasoning.
Learning objectives
What you should be able to do
- Represent and solve add and subtract mixed numbers with like denominators problems using accurate mathematical models, notation, and reasoning.
- Explain why a strategy for add and subtract mixed numbers 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 and Subtract Mixed Numbers with Like Denominators is a fractions & decimals idea built from precise quantities, representations, and operations. The mathematical goal is to preserve the meaning of each quantity while choosing a representation that makes the relationship visible.
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 and subtract mixed numbers 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 1/4 + 2 3/4.
5/4 + 11/4 = 16/4Convert mixed numbers to equivalent fractional amounts with the same denominator, combine, then rename if needed.
Add 2 2/5 + 1 4/5.
12/5 + 9/5 = 21/5Convert mixed numbers to equivalent fractional amounts with the same denominator, combine, then rename if needed.
Add 3 3/6 + 2 5/6.
21/6 + 17/6 = 38/6Convert mixed numbers to equivalent fractional amounts with the same denominator, combine, then rename if needed.
Add 1 4/7 + 1 6/7.
11/7 + 13/7 = 24/7Convert mixed numbers to equivalent fractional amounts with the same denominator, combine, then rename if needed.
Add 2 5/8 + 2 7/8.
21/8 + 23/8 = 44/8Convert mixed numbers to equivalent fractional amounts with the same denominator, combine, then rename if needed.
Add 3 3/4 + 1 2/4.
15/4 + 6/4 = 21/4Convert mixed numbers to equivalent fractional amounts with the same denominator, combine, then rename if needed.
Add 1 3/5 + 2 1/5.
8/5 + 11/5 = 19/5Convert mixed numbers to equivalent fractional amounts with the same denominator, combine, then rename if needed.
Add 2 3/6 + 1 5/6.
15/6 + 11/6 = 26/6Convert mixed numbers to equivalent fractional amounts with the same denominator, combine, then rename if needed.
Add 3 3/7 + 2 5/7.
24/7 + 19/7 = 43/7Convert mixed numbers to equivalent fractional amounts with the same denominator, combine, then rename if needed.
Add 1 3/8 + 1 5/8.
11/8 + 13/8 = 24/8Convert mixed numbers to equivalent fractional amounts with the same denominator, combine, then rename if needed.
Add 2 2/4 + 2 1/4.
10/4 + 9/4 = 19/4Convert mixed numbers to equivalent fractional amounts with the same denominator, combine, then rename if needed.
Add 3 4/5 + 1 2/5.
19/5 + 7/5 = 26/5Convert mixed numbers to equivalent fractional amounts with the same denominator, combine, then rename if needed.
Add 1 3/6 + 2 5/6.
9/6 + 17/6 = 26/6Convert mixed numbers to equivalent fractional amounts with the same denominator, combine, then rename if needed.
Add 2 2/7 + 1 4/7.
16/7 + 11/7 = 27/7Convert mixed numbers to equivalent fractional amounts with the same denominator, combine, then rename if needed.
Add 3 1/8 + 2 3/8.
25/8 + 19/8 = 44/8Convert mixed numbers to equivalent fractional amounts with the same denominator, combine, then rename if needed.
Add 1 1/4 + 1 3/4.
5/4 + 7/4 = 12/4Convert mixed numbers to equivalent fractional amounts with the same denominator, combine, then rename if needed.
Add 2 1/5 + 2 3/5.
11/5 + 13/5 = 24/5Convert mixed numbers to equivalent fractional amounts with the same denominator, combine, then rename if needed.
Add 3 3/6 + 1 5/6.
21/6 + 11/6 = 32/6Convert mixed numbers to equivalent fractional amounts with the same denominator, combine, then rename if needed.
Add 1 1/7 + 2 3/7.
8/7 + 17/7 = 25/7Convert mixed numbers to equivalent fractional amounts with the same denominator, combine, then rename if needed.
Add 2 6/8 + 1 1/8.
22/8 + 9/8 = 31/8Convert mixed numbers to equivalent fractional amounts with the same denominator, combine, then rename if needed.
Practice
Guided practice with hints
01Add 3 3/4 + 2 2/4.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 15/4 + 10/4 = 25/4
02Add 1 2/5 + 1 4/5.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 7/5 + 9/5 = 16/5
03Add 2 3/6 + 2 5/6.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 15/6 + 17/6 = 32/6
04Add 3 6/7 + 1 2/7.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 27/7 + 9/7 = 36/7
05Add 1 4/8 + 2 6/8.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 12/8 + 22/8 = 34/8
06Add 2 2/4 + 1 1/4.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 10/4 + 5/4 = 15/4
Practice
Independent practice
01Add 3 3/5 + 2 1/5.
Answer: 18/5 + 11/5 = 29/5
02Add 1 3/6 + 1 5/6.
Answer: 9/6 + 11/6 = 20/6
03Add 2 5/7 + 2 1/7.
Answer: 19/7 + 15/7 = 34/7
04Add 3 2/8 + 1 4/8.
Answer: 26/8 + 12/8 = 38/8
05Add 1 1/4 + 2 3/4.
Answer: 5/4 + 11/4 = 16/4
06Add 2 2/5 + 1 4/5.
Answer: 12/5 + 9/5 = 21/5
07Add 3 3/6 + 2 5/6.
Answer: 21/6 + 17/6 = 38/6
08Add 1 4/7 + 1 6/7.
Answer: 11/7 + 13/7 = 24/7
Common mistakes
Learn to catch the error, not just the answer.
Identify what each number represents and how the quantities are related before selecting an operation.
Estimate, use an inverse operation, or compare with a second representation.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Use add and subtract mixed numbers with like denominators when solving multi-step problems in measurement, data, money, design, or everyday quantitative decisions.
- Explain the result with units and a second check so another person can audit the reasoning.
Challenge problems
Add 2 5/8 + 2 7/8.
21/8 + 23/8 = 44/8
Add 3 3/4 + 1 2/4.
15/4 + 6/4 = 21/4
Add 1 3/5 + 2 1/5.
8/5 + 11/5 = 19/5
Add 2 3/6 + 1 5/6.
15/6 + 11/6 = 26/6
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Grade 4 Math Strategy Sprint
Solve and explain add and subtract mixed numbers with like denominators problems accurately, then check each result with a second method.
Practice
Mastery check
01Add 3 3/7 + 2 5/7.
Answer: 24/7 + 19/7 = 43/7
02Add 1 3/8 + 1 5/8.
Answer: 11/8 + 13/8 = 24/8
03Add 2 2/4 + 2 1/4.
Answer: 10/4 + 9/4 = 19/4
04Add 3 4/5 + 1 2/5.
Answer: 19/5 + 7/5 = 26/5
05Add 1 3/6 + 2 5/6.
Answer: 9/6 + 17/6 = 26/6
06Add 2 2/7 + 1 4/7.
Answer: 16/7 + 11/7 = 27/7
07Add 3 1/8 + 2 3/8.
Answer: 25/8 + 19/8 = 44/8
08Add 1 1/4 + 1 3/4.
Answer: 5/4 + 7/4 = 12/4
Terminology
Words to know
- representation
- A diagram, model, equation, table, graph, or other form showing a mathematical idea.
- strategy
- A purposeful method chosen to solve or analyze a problem.
- estimate
- A nearby value used to judge size or reasonableness.
- verify
- To confirm a result using a second calculation, representation, or logical check.
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.