Quiz Answer Key

Name:

Date:

📚 Part 1: Multiple Choice — Answers

1. 3/4 ÷ 1/2 = ?

1 1/2 — Correct

2/3

3/8

1/6

Work: 3/4 ÷ 1/2 = 3/4 × 2/1 = 3/2 = 1 1/2.

2. -2 ÷ 1/4 = ?

-8 — Correct

-1/8

-0.5

Work: -2 ÷ 1/4 = -2 × 4 = -8.

3. 4.5 ÷ 0.5 = ?

9 — Correct

0.9

2.25

Work: Dividing by 0.5 (1/2) doubles the number: 4.5 ÷ 0.5 = 9.

4. (5/6) ÷ (10/9) = ?

3/4 — Correct

9/10

5/12

6/5

Work: (5/6) × (9/10) = 45/60 = 3/4.

5. Check all that apply:

Dividing by a fraction is the same as multiplying by its reciprocal. — Correct

Dividing by zero is undefined. — Correct

The reciprocal of -2/5 is -5/2. — Correct

If you divide by a positive number less than 1, the result is smaller. — Incorrect

Note: Dividing by a positive fraction less than 1 multiplies by a number greater than 1, so the result is larger.

✏️ Part 2: Short Answers & Word Problems — Answers

6. A recipe needs 3/8 cup sugar per batch. You have 2 cups. How many full batches can you make?

Answer: 2 ÷ 3/8 = 2 × 8/3 = 16/3 = 5 1/3, so you can make 5 full batches.

7. A diver goes down a total of -72 feet in 3 equal dives. How many feet does the diver descend each dive?

Answer: -72 ÷ 3 = -24 feet per dive.

8. Calculate: 0.025 ÷ 0.5 = ________

Answer: 0.025 ÷ 0.5 = 0.05 (dividing by 0.5 doubles the number).

9. Explain in one sentence: Why does dividing by a positive fraction less than 1 give a larger result?

Answer: Because dividing by a fraction <1 is the same as multiplying by its reciprocal (a number >1), so the result increases.

🧾 Teacher Notes & Supports

I can... statements: I can divide positive and negative rational numbers, including fractions and decimals; I can solve real-world problems by dividing rational numbers and explain my reasoning.

Success criteria: Accurately compute quotients for fractions, decimals, and integers; show steps using reciprocals when dividing by fractions; apply division to at least one real-world problem correctly.

Differentiation strategies: Provide fraction strips or visual models for learners who need concrete supports; offer step-by-step scaffolded notes (reciprocal rule reminder) and allow calculator checks for accuracy.

Extension activities: Create multi-step problems that combine division of rationals with unit conversions (e.g., miles per gallon, cost per ounce); explore dividing rational expressions or word problems with negative rates.

Dyslexia-friendly options: Provide printed copies with larger fonts and increased spacing; read problems aloud and allow oral responses or dictation tools.