Question

extra practice:
evaluate expressions with grouping symbols
evaluate the expression.

1. $16 \div (2 \times 2) + (3 \times 4)$
2. $5 \times (3 + 8) - (7 + 4)$
3. $(8 \times 5) \div (3 + 9 + 8)$
4. $(21 - 14) \times (16 \div 8)$
5. $(10 - 8) + (12 - 4) \times 2$
6. $(13 - 5) \div (8 - 6) \times 9$
7. $(14 - 9) \times (12 - 6) \div 10$
8. $5 \times (7 + 8) - 10$
9. $75 \div (105 + 20) \div 5$
10. $20 \div (24 - 20) \times 5$
11. $4 + 16 \div 8 + (7 - 3) + 3$
12. $8 \times \\{(20 - 9 \div 3 - 9) + 2 \times 10\\}$

Explanation:

Let's solve each expression step by step following the order of operations (PEMDAS/BODMAS: Parentheses/Brackets, Exponents/Orders, Multiplication and Division - left to right, Addition and Subtraction - left to right).

1. \( 16 \div (2 \times 2) + (3 \times 4) \)

Step 1: Evaluate inside parentheses

First, calculate the values inside the parentheses: \( 2 \times 2 = 4 \) and \( 3 \times 4 = 12 \).

Step 2: Perform division and addition

Now, perform the division: \( 16 \div 4 = 4 \). Then add the results: \( 4 + 12 = 16 \).

2. \( 5 \times (3 + 8) - (7 + 4) \)

Step 1: Evaluate inside parentheses

Calculate the values inside the parentheses: \( 3 + 8 = 11 \) and \( 7 + 4 = 11 \).

Step 2: Perform multiplication and subtraction

Perform the multiplication: \( 5 \times 11 = 55 \). Then subtract: \( 55 - 11 = 44 \).

3. \( (8 \times 5) \div (3 + 9 + 8) \)

Step 1: Evaluate inside parentheses

Calculate the values inside the parentheses: \( 8 \times 5 = 40 \) and \( 3 + 9 + 8 = 20 \).

Step 2: Perform division

Divide the results: \( 40 \div 20 = 2 \).

4. \( (21 - 14) \times (16 \div 8) \)

Step 1: Evaluate inside parentheses

Calculate the values inside the parentheses: \( 21 - 14 = 7 \) and \( 16 \div 8 = 2 \).

Step 2: Perform multiplication

Multiply the results: \( 7 \times 2 = 14 \).

5. \( [(10 - 8) + (12 - 4)] \times 2 \)

Step 1: Evaluate inside the innermost parentheses

Calculate the values inside the innermost parentheses: \( 10 - 8 = 2 \) and \( 12 - 4 = 8 \).

Step 2: Evaluate inside the brackets

Add the results inside the brackets: \( 2 + 8 = 10 \).

Step 3: Perform multiplication

Multiply by 2: \( 10 \times 2 = 20 \).

6. \( [(13 - 5) \div (8 - 6)] \times 9 \)

Step 1: Evaluate inside the innermost parentheses

Calculate the values inside the innermost parentheses: \( 13 - 5 = 8 \) and \( 8 - 6 = 2 \).

Step 2: Evaluate inside the brackets

Divide the results inside the brackets: \( 8 \div 2 = 4 \).

Step 3: Perform multiplication

Multiply by 9: \( 4 \times 9 = 36 \).

7. \( [(14 - 9) \times (12 - 6)] \div 10 \)

Step 1: Evaluate inside the innermost parentheses

Calculate the values inside the innermost parentheses: \( 14 - 9 = 5 \) and \( 12 - 6 = 6 \).

Step 2: Evaluate inside the brackets

Multiply the results inside the brackets: \( 5 \times 6 = 30 \).

Step 3: Perform division

Divide by 10: \( 30 \div 10 = 3 \).

8. \( 5 \times [(7 + 8) - 10] \)

Step 1: Evaluate inside the innermost parentheses

Calculate the value inside the innermost parentheses: \( 7 + 8 = 15 \).

Step 2: Evaluate inside the brackets

Subtract 10 from the result: \( 15 - 10 = 5 \).

Step 3: Perform multiplication

Multiply by 5: \( 5 \times 5 = 25 \).

9. \( 75 \div [(105 + 20) \div 5] \)

Step 1: Evaluate inside the innermost parentheses

Calculate the value inside the innermost parentheses: \( 105 + 20 = 125 \).

Step 2: Evaluate inside the brackets

Divide the result by 5: \( 125 \div 5 = 25 \).

Step 3: Perform division

Divide 75 by the result: \( 75 \div 25 = 3 \).

10. \( 20 \div [(24 - 20) \times 5] \)

Step 1: Evaluate inside the innermost parentheses

Calculate the value inside the innermost parentheses: \( 24 - 20 = 4 \).

Step 2: Evaluate inside the brackets

Multiply the result by 5: \( 4 \times 5 = 20 \).

Step 3: Perform division

Divide 20 by the result: \( 20 \div 20 = 1 \).

11. \( 4 + [16 \div 8 + (7 - 3)] + 3 \)

Step 1: Evaluate inside the innermost parentheses

Calculate the value inside the innermost parentheses: \( 7 - 3 = 4 \).

Step 2: Evaluate inside the brackets

Perform the division and addition inside the brackets: \( 16 \div 8 = 2 \), then \( 2 + 4 = 6 \).

Step 3: Perform addition

Add the results: \( 4 + 6 + 3 = 13 \).

12. \( 8 \times \{[(20 - 9 \div 3 - 9) + 2] \times 10\} \)

Step 1: Evaluate inside the innermost parentheses (perform division first)

First, perform the division: \( 9 \div 3 = 3 \). Then calculate inside the innermost parentheses: \( 20 - 3 - 9 = 8 \).

Step 2: Evaluate inside the brackets

Add 2 to the result: \( 8 + 2 = 10 \).

Step 3: Evaluate inside the braces

Multiply the result by 10: \( 10 \times 10 = 100 \).

Step 4: Perform multiplication

Multiply by 8: \( 8 \times 100 = 800 \).

Answers:

1. \( \boldsymbol{16} \)
2. \( \boldsymbol{44} \)
3. \( \boldsymbol{2} \)
4. \( \boldsymbol{14} \)
5. \( \boldsymbol{20} \)
6. \( \boldsymbol{36} \)
7. \( \boldsymbol{3} \)
8. \( \boldsymbol{25} \)
9. \( \boldsymbol{3} \)
10. \( \boldsymbol{1} \)
11. \( \boldsymbol{13} \)
12. \( \boldsymbol{800} \)

Answer:

s:

1. \( \boldsymbol{16} \)
2. \( \boldsymbol{44} \)
3. \( \boldsymbol{2} \)
4. \( \boldsymbol{14} \)
5. \( \boldsymbol{20} \)
6. \( \boldsymbol{36} \)
7. \( \boldsymbol{3} \)
8. \( \boldsymbol{25} \)
9. \( \boldsymbol{3} \)
10. \( \boldsymbol{1} \)
11. \( \boldsymbol{13} \)
12. \( \boldsymbol{800} \)