Answer Key with Explanations

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📚 Part 1: Multiple Choice & Matching — Answer Key

1. What is 1/2 + 1/4?

1/2

3/4

2/3

1/6

Explanation: Convert to common denominator 4: 2/4 + 1/4 = 3/4.

2. What is 3/4 − 1/3?

5/12

1/4

1/2

2/3

Explanation: Common denominator 12: 9/12 − 4/12 = 5/12.

3. What is 2/3 × 3/4?

1/2

5/6

1/3

3/7

Explanation: Multiply numerators and denominators: (2×3)/(3×4)=6/12=1/2. You can cancel the 3 first (2/1 × 1/4 = 2/4 = 1/2).

4. What is (1/2) ÷ (1/4)?

1/2

1/4

Explanation: Divide by a fraction = multiply by its reciprocal: 1/2 × 4/1 = 4/2 = 2. (Correct choice is 2.)

5. Match each expression with its simplified answer. Draw a line to match.

A. 3/5 + 1/5

B. 5/6 − 1/2

C. 4/9 × 2/3

D. 2 ÷ 3/8

1. 4/5

2. 1/3

3. 8/27

4. 16/3

Matches & Explanations: A → 1 (3/5+1/5=4/5). B → 2 (5/6−3/6=2/6=1/3). C → 3 (4/9×2/3=8/27). D → 4 (2×8/3=16/3).

✏️ Part 2: Short Answers — Answer Key & Explanations

6. Simplify: 7/8 − 1/4 = _________

Convert 1/4 to eighths: 1/4 = 2/8. Subtract: 7/8 − 2/8 = 5/8.

Answer: 5/8

7. Multiply and simplify: 1 1/2 × 2/3 = _________

Convert to improper: 1 1/2 = 3/2. Multiply: (3/2) × (2/3) = (3×2)/(2×3) = 6/6 = 1.

Answer: 1

8. Word problem: A cookie recipe needs 3/4 cup sugar. If you make 3 batches, how many cups of sugar total? Show your work and give a mixed number if needed.

Total sugar = 3 × (3/4) = 9/4. Convert to mixed number: 9/4 = 2 1/4 cups.

Answer: 2 1/4 cups

9. Measurement: A 3-mile trail is divided into 5 equal parts. What fraction of a mile is each part? _________ mile

Each part = 3 ÷ 5 = 3/5 mile.

Answer: 3/5 mile

Teacher Notes

I can... add, subtract, multiply, and divide fractions and simplify my answers.

Success criteria: Find common denominators for add/subtract, multiply numerators and denominators, use reciprocals for division, and simplify final answers.

Differentiation strategies: Provide fraction strips or a number line and offer step-by-step prompts (e.g., "find common denominator" → "convert" → "compute" → "simplify") for students who need concrete supports.

Extension activity: Create and solve two real-life word problems that use mixed numbers and improper fractions. Swap with a partner and check each other's work.

Dyslexia-friendly options: Use colored overlays or a ruler to track lines, read problems aloud, break multi-step questions into numbered steps, and highlight key numbers and operation words.