Evaluate `8+30-:2+4`. Insert a bracket such that expression becomes equal to:
a. 13 b. 23

Answer

To solve the problem of inserting brackets in the expression `8 + 30 ÷ 2 + 4` to achieve the results of 13 and 23, we will evaluate the expression step by step.

### Step-by-Step Solution:

1. **Understanding the Expression**:
The original expression is `8 + 30 ÷ 2 + 4`. We need to insert brackets to change the order of operations.

2. **Finding the Result for 23**:
- Let's try inserting brackets around `8 + 30`:
\[ (8 + 30) ÷ 2 + 4 \]
- Calculate inside the bracket first:
\[ 8 + 30 = 38 \]
- Now substitute back into the expression:
\[ 38 ÷ 2 + 4 \]
- Divide:
\[ 38 ÷ 2 = 19 \]
- Now add 4:
\[ 19 + 4 = 23 \]
- Thus, we have found that inserting brackets as `(8 + 30) ÷ 2 + 4` gives us 23.

3. **Finding the Result for 13**:
- Now, let's try inserting brackets around `30 ÷ 2 + 4`:
\[ 8 + (30 ÷ 2 + 4) \]
- Calculate inside the bracket first:
\[ 30 ÷ 2 = 15 \]
- Now substitute back into the expression:
\[ 8 + (15 + 4) \]
- Add inside the bracket:
\[ 15 + 4 = 19 \]
- Now add 8:
\[ 8 + 19 = 27 \]
- This does not yield 13, so we need to try another arrangement.

4. **Trying Another Arrangement for 13**:
- Let's try inserting brackets around `2 + 4`:
\[ 8 + 30 ÷ (2 + 4) \]
- Calculate inside the bracket:
\[ 2 + 4 = 6 \]
- Substitute back into the expression:
\[ 8 + 30 ÷ 6 \]
- Divide:
\[ 30 ÷ 6 = 5 \]
- Now add 8:
\[ 8 + 5 = 13 \]
- Thus, we have found that inserting brackets as `8 + 30 ÷ (2 + 4)` gives us 13.

### Final Results:
- For part a (result = 13): The expression is `8 + 30 ÷ (2 + 4)`.
- For part b (result = 23): The expression is `(8 + 30) ÷ 2 + 4`.