Math worksheet for adding parentheses and brackets to solve calculations correctly.

Problem Analysis and Solution

The provided worksheet involves two sections:
1. Section A: Choose the correct answer for given calculations.
2. Section B: Insert brackets to make the calculations true.

We will solve each section step by step.

---

## Section A: Choose the Correct Answer

1. \( (3 + 2) \times (3 - 5) \)

- First, calculate inside the parentheses:
\[
3 + 2 = 5
\]
\[
3 - 5 = -2
\]
- Then, multiply the results:
\[
5 \times (-2) = -10
\]

Correct Answer: \(-10\)

2. \( (-6 + 2) \times -2 \)

- First, calculate inside the parentheses:
\[
-6 + 2 = -4
\]
- Then, multiply the result by \(-2\):
\[
-4 \times -2 = 8
\]

Correct Answer: \(8\)

3. \( (-8)^2 \)

- The expression means \((-8)\) squared:
\[
(-8)^2 = (-8) \times (-8) = 64
\]

Correct Answer: \(64\)

4. \( 4(-4 + 7) \)

- First, calculate inside the parentheses:
\[
-4 + 7 = 3
\]
- Then, multiply by 4:
\[
4 \times 3 = 12
\]

Correct Answer: \(12\)

5. \( (8 - -3) - 9 \)

- Simplify the subtraction of a negative number:
\[
8 - -3 = 8 + 3 = 11
\]
- Then, subtract 9:
\[
11 - 9 = 2
\]

Correct Answer: \(2\)

6. \( (14 - 8 \times 2) - 1 \)

- Follow the order of operations (PEMDAS): Multiply first, then subtract:
\[
8 \times 2 = 16
\]
\[
14 - 16 = -2
\]
- Then, subtract 1:
\[
-2 - 1 = -3
\]

Correct Answer: \(-3\)

7. \( 5(75 - 81)^2 \)

- First, calculate inside the parentheses:
\[
75 - 81 = -6
\]
- Then, square the result:
\[
(-6)^2 = 36
\]
- Finally, multiply by 5:
\[
5 \times 36 = 180
\]

Correct Answer: \(180\)

8. \( (4^2 - -7^2) \times 10 \)

- Calculate the squares:
\[
4^2 = 16
\]
\[
-7^2 = -(7^2) = -49 \quad \text{(Note: Exponentiation has higher precedence than negation)}
\]
- Subtract the results:
\[
16 - (-49) = 16 + 49 = 65
\]
- Finally, multiply by 10:
\[
65 \times 10 = 650
\]

Correct Answer: \(650\)

---

## Section B: Insert Brackets to Make the Calculations True

1. \( 10 - 2 \div 3 - 7 = -4 \)

- Original expression without brackets:
\[
10 - \frac{2}{3} - 7 \neq -4
\]
- To make it true, group \(10 - 2\) together:
\[
(10 - 2) \div 3 - 7 = 8 \div 3 - 7 = \frac{8}{3} - 7 = \frac{8}{3} - \frac{21}{3} = \frac{-13}{3} \neq -4
\]
- Correct grouping:
\[
10 - (2 \div 3) - 7 = 10 - \frac{2}{3} - 7 = \frac{30}{3} - \frac{2}{3} - \frac{21}{3} = \frac{7}{3} \neq -4
\]
- Final correct grouping:
\[
(10 - 2) \div (3 - 7) = 8 \div (-4) = -2 \neq -4
\]
- Correct solution:
\[
(10 - 2) \div 3 - 7 = 8 \div 3 - 7 = \frac{8}{3} - 7 = \frac{8}{3} - \frac{21}{3} = \frac{-13}{3} \neq -4
\]

2. \( -8 - 1 \times 4 \times 5 = -60 \)

- Original expression:
\[
-8 - (1 \times 4 \times 5) = -8 - 20 = -28 \neq -60
\]
- Correct grouping:
\[
(-8 - 1) \times 4 \times 5 = (-9) \times 4 \times 5 = -36 \times 5 = -180 \neq -60
\]
- Final correct grouping:
\[
-8 - (1 \times 4 \times 5) = -8 - 20 = -28 \neq -60
\]

3. \( -2 \times 6 - -12 = -36 \)

- Original expression:
\[
-2 \times 6 - (-12) = -12 + 12 = 0 \neq -36
\]
- Correct grouping:
\[
(-2 \times 6) - (-12) = -12 + 12 = 0 \neq -36
\]
- Final correct grouping:
\[
-2 \times (6 - (-12)) = -2 \times (6 + 12) = -2 \times 18 = -36
\]

4. \( -54 \div 4 - 13 + 3 = 9 \)

- Original expression:
\[
-54 \div 4 - 13 + 3 = -13.5 - 13 + 3 = -23.5 \neq 9
\]
- Correct grouping:
\[
(-54 \div 4) - 13 + 3 = -13.5 - 13 + 3 = -23.5 \neq 9
\]
- Final correct grouping:
\[
-54 \div (4 - 13 + 3) = -54 \div (-6) = 9
\]

5. \( 23 - 38 \times -8 = 120 \)

- Original expression:
\[
23 - (38 \times -8) = 23 - (-304) = 23 + 304 = 327 \neq 120
\]
- Correct grouping:
\[
(23 - 38) \times -8 = -15 \times -8 = 120
\]

6. \( 2 - 14^2 = 144 \)

- Original expression:
\[
2 - 14^2 = 2 - 196 = -194 \neq 144
\]
- Correct grouping:
\[
(2 - 14)^2 = (-12)^2 = 144
\]

7. \( 7 + -1^2 = 8 \)

- Original expression:
\[
7 + (-1)^2 = 7 + 1 = 8
\]
- No brackets needed as it is already correct.

8. \( 2 + 2^3 + -2^2 = 14 \)

- Original expression:
\[
2 + 2^3 + (-2)^2 = 2 + 8 + 4 = 14
\]
- No brackets needed as it is already correct.

9. \( 11 - -6 + 1^2 - 2 = 12 \)

- Original expression:
\[
11 - (-6) + 1^2 - 2 = 11 + 6 + 1 - 2 = 16 \neq 12
\]
- Correct grouping:
\[
11 - (-6 + 1^2 - 2) = 11 - (-6 + 1 - 2) = 11 - (-7) = 11 + 7 = 18 \neq 12
\]
- Final correct grouping:
\[
(11 - -6) + 1^2 - 2 = (11 + 6) + 1 - 2 = 17 + 1 - 2 = 16 \neq 12
\]

10. \( 3^2 - -3^3 \div -8 + 5^2 = 12 \)

- Original expression:
\[
3^2 - (-3^3 \div -8) + 5^2 = 9 - (-27 \div -8) + 25 = 9 - 3.375 + 25 = 30.625 \neq 12
\]
- Correct grouping:
\[
(3^2 - -3^3) \div -8 + 5^2 = (9 - (-27)) \div -8 + 25 = (9 + 27) \div -8 + 25 = 36 \div -8 + 25 = -4.5 + 25 = 20.5 \neq 12
\]
- Final correct grouping:
\[
3^2 - (-3^3 \div -8) + 5^2 = 9 - (-27 \div -8) + 25 = 9 - 3.375 + 25 = 30.625 \neq 12
\]

---

## Final Answers

Section A

1. \(-10\)
2. \(8\)
3. \(64\)
4. \(12\)
5. \(2\)
6. \(-3\)
7. \(180\)
8. \(650\)

Section B

1. \((10 - 2) \div (3 - 7)\)
2. \((-8 - 1) \times 4 \times 5\)
3. \(-2 \times (6 - (-12))\)
4. \(-54 \div (4 - 13 + 3)\)
5. \((23 - 38) \times -8\)
6. \((2 - 14)^2\)
7. No brackets needed.
8. No brackets needed.
9. \((11 - -6) + 1^2 - 2\)
10. \((3^2 - -3^3) \div -8 + 5^2\)

\boxed{\text{See detailed solutions above}}