Fractions and Probability Operations

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🔢 Part 1: Multiplying and Dividing Fractions

1. Calculate 2/3 × 3/4. Show your working.

2. Work out 1 3/5 × 2/3. (Convert to improper fractions first)

3. Calculate 5/8 ÷ 3/4 by multiplying by the reciprocal.

4. Which of these is equivalent to 2/5 ÷ 3/7?

2/5 × 3/7

2/5 × 7/3

5/2 × 3/7

7/3 × 5/2

🎲 Part 2: Probability with Fractions

5. A spinner has 8 equal sections: 3 red, 2 blue, and 3 green. What is the probability of spinning red then blue? (Write as a fraction in simplest form)

6. A bag contains 5 red balls and 3 blue balls. One ball is drawn and not replaced. What is the probability the second ball drawn is red?

7. The probability of rain on Monday is 2/5. The probability of rain on Tuesday is 1/3. If these events are independent, what is the probability it rains on both days?

🧠 Part 3: Problem Solving

8. A recipe calls for 2 1/4 cups of flour. If you want to make 2/3 of the recipe, how much flour do you need? Show all working.

9. In a game, the probability of winning the first round is 3/4. If you win the first round, the probability of winning the second round is 2/5. What is the probability of winning both rounds?

10. A box contains 12 chocolates: 7 milk chocolate and 5 dark chocolate. Two chocolates are eaten (without replacement). Calculate the probability that both chocolates are milk chocolate.

11. Explain in your own words why we multiply by the reciprocal when dividing fractions.