Quiz Answers and Explanations

Name:

Date:

📚 Part 1: Multiple Choice — Answers & Explanations

1. What is 2 1/2 ÷ 3/4?

1 3/4

3 1/3

5/6

Answer: 3 1/3. Explanation: 2 1/2 = 5/2. Compute 5/2 ÷ 3/4 = 5/2 × 4/3 = 20/6 = 10/3 = 3 1/3.

2. What is 3 3/4 ÷ 1 1/2?

2 1/2

5/4

1 1/4

Answer: 2 1/2. Explanation: 3 3/4 = 15/4 and 1 1/2 = 3/2. 15/4 × 2/3 = 30/12 = 5/2 = 2 1/2.

3. What is 1 2/3 ÷ 5?

1/3

1/5

5/3

Answer: 1/3. Explanation: 1 2/3 = 5/3. 5/3 ÷ 5 = 5/3 × 1/5 = 1/3.

4. A recipe uses 2 2/3 cups per pan. With 8 cups, how many full pans?

2 pans

3 pans

3 1/3 pans

2 2/3 pans

Answer: 3 pans. Explanation: 2 2/3 = 8/3. 8 ÷ (8/3) = 8 × 3/8 = 3 full pans.

✏️ Part 2: Short Answers — Solutions & Work

5. Compute and simplify: 4 1/2 ÷ 2 3/4. Show your work.

4 1/2 = 9/2 ; 2 3/4 = 11/4

9/2 ÷ 11/4 = 9/2 × 4/11 = 36/22 = 18/11

18/11 = 1 7/11

Final answer: 1 7/11

6. A ribbon 7 1/4 ft long is cut into pieces 1 1/2 ft each. How many full pieces? How much left over?

7 1/4 = 29/4 ; 1 1/2 = 3/2

29/4 ÷ 3/2 = 29/4 × 2/3 = 58/12 = 29/6 = 4 5/6

Full pieces: 4

Leftover: 5/6 ft. In inches: 5/6 × 12 = 10 inches.

7. If a student reads 2 1/3 books per month, how many months to read 5 books? Give answer as a mixed number.

2 1/3 = 7/3 books/month

Months = 5 ÷ (7/3) = 5 × 3/7 = 15/7 = 2 1/7

Final answer: 2 1/7 months

8. Explain the steps you use to divide mixed numbers (2–3 sentences).

Convert mixed numbers to improper fractions, then change the division to multiplication by flipping (reciprocal) the divisor. Multiply numerators and denominators, simplify the result, and convert any improper fraction back to a mixed number. Check by estimating or using a calculator if needed.

🛠 Supports & Extension

I can: Divide mixed numbers by fractions and mixed numbers.

Success criteria: Convert mixed numbers to improper fractions → invert the divisor → multiply → simplify → convert to mixed form when appropriate.

Differentiation strategies: Provide fraction strips or visual models; allow a calculator for checking; give one-on-one guided practice converting mixed numbers.

Extension activities: Express answers as decimals; create rate word problems (e.g., miles per hour) that require dividing mixed numbers.

Dyslexia-friendly options: Use larger font and increased spacing, read problems aloud, and highlight key numbers and operation words.