Calculate the value of the expression:

$$15 \div 3 ext{ of } 2 imes 2 + 9 \div 18 ext{ of } 2 imes 4 - 4 \div 8 imes 2$$

Question

Calculate the value of the expression:

$$15 \div 3 	ext{ of } 2 	imes 2 + 9 \div 18 	ext{ of } 2 	imes 4 - 4 \div 8 	imes 2$$

Accepted Answer

**Solution:**

1. Understand that "of" means multiplication.

2. Rewrite the expression clearly:
   $$15 \div 3 	imes 2 	imes 2 + 9 \div 18 	imes 2 	imes 4 - 4 \div 8 	imes 2$$

3. Calculate each part step-by-step following BODMAS (Brackets, Orders, Division and Multiplication from left to right, Addition and Subtraction):

- First part: $$15 \div 3 	imes 2 	imes 2$$
  - $$15 \div 3 = 5$$
  - $$5 	imes 2 = 10$$
  - $$10 	imes 2 = 20$$

- Second part: $$9 \div 18 	imes 2 	imes 4$$
  - $$9 \div 18 = \frac{9}{18} = \frac{1}{2}$$
  - $$\frac{1}{2} 	imes 2 = 1$$
  - $$1 	imes 4 = 4$$

- Third part: $$4 \div 8 	imes 2$$
  - $$4 \div 8 = \frac{4}{8} = \frac{1}{2}$$
  - $$\frac{1}{2} 	imes 2 = 1$$

4. Now combine all parts:
   $$20 + 4 - 1 = 23$$

This result (23) does not match any options, so let's carefully re-check the original expression and the interpretation of "of".

**Re-examining the expression:**
The original expression is:

$$15 \div 3 	ext{ of } 2 	imes 2 + 9 \div 18 	ext{ of } 2 	imes 4 - 4 \div 8 	imes 2$$

"of" means multiplication, but the division and multiplication must be handled carefully.

Let's rewrite with parentheses to clarify:

$$\left(15 \div (3 	imes 2) 	imes 2ight) + \left(9 \div (18 	imes 2) 	imes 4ight) - \left(4 \div 8 	imes 2ight)$$

Check if "of" applies to the number immediately after division:

- First term: 15 ÷ 3 of 2 × 2
  - "3 of 2" means 3 × 2 = 6
  - So, 15 ÷ 6 × 2
  - 15 ÷ 6 = 2.5
  - 2.5 × 2 = 5

- Second term: 9 ÷ 18 of 2 × 4
  - "18 of 2" means 18 × 2 = 36
  - 9 ÷ 36 × 4
  - 9 ÷ 36 = 0.25
  - 0.25 × 4 = 1

- Third term: 4 ÷ 8 × 2
  - 4 ÷ 8 = 0.5
  - 0.5 × 2 = 1

Now sum all:

$$5 + 1 - 1 = 5$$

5 is one of the options.

**Answer:** 5

**Note:** The key was to interpret "of" as multiplication and apply it immediately after the divisor, changing the divisor to a product before division.

Hence, the correct answer is option 2: 5.

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