Explore · unlike fractions
Compute 5/6 − 1/4. Show equivalent fractions with a common denominator.
Great Inheritance Mathematics Term A · Independent learning
Subtracting Unlike Fractions
Learning target: Rename unlike fractions equivalently before subtraction and verify reasonableness.
Begin with the exact prerequisite checkpoint below. Afterward, explain why your strategy works, not merely which procedure to use.
Opening task
Lesson-specific prerequisite checkpoint
Do this without a worked example. If you cannot explain it, review the earlier skill before continuing.
Which is larger, 3/4 or 1/2?
Understand the idea
Rename unlike fractions equivalently before subtraction and verify reasonableness.
Before subtracting unlike fractions, divide the same-size whole into common-sized parts. Subtract numerator counts only after denominators match. Use a number line to confirm that a positive subtraction becomes smaller.
Vocabulary focus: same whole, equivalent fractions, mixed numbers. Make a small labeled model, work through the arithmetic, and explain the result in words.
Watch for: Subtracting numerator and denominator separately.
Model to study: Aligned fraction strips and interval diagram.
Worked examples
Worked examples 1 · unlike fractions
Compute 4/5 − 1/3. Show equivalent fractions with a common denominator.
Solution: 7/15
Why: Use 15-ths: 4/5=12/15 and 1/3=5/15. 12/15 − 5/15 = 7/15 = 7/15.
Worked examples 2 · unlike fractions
Compute 3/4 − 2/5. Show equivalent fractions with a common denominator.
Solution: 7/20
Why: Use 20-ths: 3/4=15/20 and 2/5=8/20. 15/20 − 8/20 = 7/20 = 7/20.
Worked examples 3 · unlike fractions
Compute 3/4 − 1/3. Show equivalent fractions with a common denominator.
Solution: 5/12
Why: Use 12-ths: 3/4=9/12 and 1/3=4/12. 9/12 − 4/12 = 5/12 = 5/12.
Check understanding
Check understanding 1 · unlike fractions
Compute 5/6 − 3/4. Show equivalent fractions with a common denominator.
Check understanding 2 · unlike fractions
Compute 5/6 − 2/3. Show equivalent fractions with a common denominator.
Guided practice
Guided practice 1 · unlike fractions
Compute 1/2 − 3/8. Show equivalent fractions with a common denominator.
Guided practice 2 · unlike fractions
Compute 3/4 − 1/6. Show equivalent fractions with a common denominator.
Guided practice 3 · unlike fractions
Compute 1/2 − 1/3. Show equivalent fractions with a common denominator.
Independent practice
Independent practice 1 · unlike fractions
Compute 3/4 − 3/5. Show equivalent fractions with a common denominator.
Independent practice 2 · unlike fractions
Compute 2/3 − 3/5. Show equivalent fractions with a common denominator.
Independent practice 3 · unlike fractions
Compute 1/3 − 1/8. Show equivalent fractions with a common denominator.
Independent practice 4 · unlike fractions
Compute 4/5 − 3/4. Show equivalent fractions with a common denominator.
Independent practice 5 · unlike fractions
Compute 3/5 − 1/3. Show equivalent fractions with a common denominator.
Challenge and error analysis
Challenge and error analysis 1 · worked-error diagnosis
Error-analysis notebook: Learner notebook (LESSON): “For 1/2 and 2/5, my answer is 3/7; I added both numerators and denominators without making equal parts.” Identify exactly which written step or assumption fails, correct it, and independently solve this new task: Compute 1/2 − 2/5. Show equivalent fractions with a common denominator.
Challenge and error analysis 2 · reasoning transfer
Reasoning and transfer: Solve, then explain a different way to check your answer (inverse operation, estimate, model, or units as appropriate). Compute 2/3 − 1/3. Show equivalent fractions with a common denominator.
Exit check
Exit check 1 · unlike fractions
Compute 1/2 − 1/8. Show equivalent fractions with a common denominator.
Exit check 2 · unlike fractions
Compute 6/7 − 5/6. Show equivalent fractions with a common denominator.
Target for independent mastery: all exit-check problems correct plus a justified explanation. A instructor may reteach the concept if calculations are correct without meaningful reasoning.