Evaluate `12+4xx3+9-:3` . Insert a bracket in the expression which makes it equal to a. 51 b. 28

Answer

To solve the expression `12 + 4 x 3 + 9 ÷ 3` and find brackets that make it equal to 51 and 28, we will follow the order of operations (BODMAS/BIDMAS rules).

### Part A: Making the expression equal to 51

1. **Insert a bracket**: We will insert a bracket around `12 + 4`.
- Expression becomes: `(12 + 4) x 3 + 9 ÷ 3`

2. **Calculate inside the bracket**:
- \( 12 + 4 = 16 \)
- New expression: `16 x 3 + 9 ÷ 3`

3. **Perform division**:
- \( 9 ÷ 3 = 3 \)
- New expression: `16 x 3 + 3`

4. **Perform multiplication**:
- \( 16 x 3 = 48 \)
- New expression: `48 + 3`

5. **Perform addition**:
- \( 48 + 3 = 51 \)

Thus, the expression evaluates to 51.

### Part B: Making the expression equal to 28

1. **Insert a bracket**: We will insert a bracket around `3 + 9`.
- Expression becomes: `12 + 4 x (3 + 9) ÷ 3`

2. **Calculate inside the bracket**:
- \( 3 + 9 = 12 \)
- New expression: `12 + 4 x 12 ÷ 3`

3. **Perform division**:
- \( 12 ÷ 3 = 4 \)
- New expression: `12 + 4 x 4`

4. **Perform multiplication**:
- \( 4 x 4 = 16 \)
- New expression: `12 + 16`

5. **Perform addition**:
- \( 12 + 16 = 28 \)

Thus, the expression evaluates to 28.

### Summary:
- For 51, the bracket is around `12 + 4`.
- For 28, the bracket is around `3 + 9`.