Explore · mixed-number subtraction
Subtract 8 1/4 − 1 1/2. Explain any exchange needed.
Singapore Math 5A · Independent learning
Subtracting Mixed Numbers— Part 2
Learning target: Rename one whole to subtract mixed-number fractional parts requiring borrowing.
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.
Show one whole as eighths.
Understand the idea
Rename one whole to subtract mixed-number fractional parts requiring borrowing.
When the first fractional part is too small, exchange one whole for denominator-sized equal parts. For example, 4 1/5 can be renamed 3 6/5. Subtract after the exchange and express the result as a simplified mixed number.
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: Adding b fractional parts without subtracting one whole.
Model to study: One-whole-for-denominator-parts exchange diagram.
Worked examples
Worked examples 1 · mixed-number subtraction
Subtract 6 1/3 − 2 2/3. Explain any exchange needed.
Solution: 3 2/3
Why: Exchange one whole in 6 1/3: 6 2/6 = 5 8/6. Subtract 2 4/6 to get 3 2/3.
Worked examples 2 · mixed-number subtraction
Subtract 5 1/4 − 1 1/2. Explain any exchange needed.
Solution: 3 3/4
Why: Exchange one whole in 5 1/4: 5 1/4 = 4 5/4. Subtract 1 2/4 to get 3 3/4.
Worked examples 3 · mixed-number subtraction
Subtract 7 1/4 − 2 3/4. Explain any exchange needed.
Solution: 4 1/2
Why: Exchange one whole in 7 1/4: 7 1/4 = 6 5/4. Subtract 2 3/4 to get 4 1/2.
Check understanding
Check understanding 1 · mixed-number subtraction
Subtract 4 1/4 − 2 1/2. Explain any exchange needed.
Check understanding 2 · mixed-number subtraction
Subtract 8 1/4 − 1 3/4. Explain any exchange needed.
Guided practice
Guided practice 1 · mixed-number subtraction
Subtract 5 1/4 − 2 3/4. Explain any exchange needed.
Guided practice 2 · mixed-number subtraction
Subtract 5 1/4 − 3 1/2. Explain any exchange needed.
Guided practice 3 · mixed-number subtraction
Subtract 7 1/6 − 1 2/3. Explain any exchange needed.
Independent practice
Independent practice 1 · mixed-number subtraction
Subtract 7 1/3 − 1 2/3. Explain any exchange needed.
Independent practice 2 · mixed-number subtraction
Subtract 6 1/4 − 3 3/4. Explain any exchange needed.
Independent practice 3 · mixed-number subtraction
Subtract 4 1/4 − 1 3/4. Explain any exchange needed.
Independent practice 4 · mixed-number subtraction
Subtract 4 1/6 − 3 2/3. Explain any exchange needed.
Independent practice 5 · mixed-number subtraction
Subtract 5 1/8 − 3 1/2. Explain any exchange needed.
Challenge and error analysis
Challenge and error analysis 1 · worked-error diagnosis
Error-analysis notebook: Learner notebook (LESSON): “For 43/6 and 11/3, my answer is 6; 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: Subtract 7 1/6 − 3 2/3. Explain any exchange needed.
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). Subtract 6 1/4 − 3 1/2. Explain any exchange needed.
Exit check
Exit check 1 · mixed-number subtraction
Subtract 8 1/4 − 3 1/2. Explain any exchange needed.
Exit check 2 · mixed-number subtraction
Subtract 7 1/4 − 3 5/8. Explain any exchange needed.
Target for independent mastery: all exit-check problems correct plus a justified explanation. A tutor may reteach the concept if calculations are correct without meaningful reasoning.