To solve the problems, we need to follow the
Order of Operations, often remembered by the acronym
PEMDAS:
-
P: Parentheses
-
E: Exponents
-
M/D: Multiplication and Division (from left to right)
-
A/S: Addition and Subtraction (from left to right)
Let's solve each problem step by step.
---
Problem 1: \( 5(3 + 5) + 20 \)
1. Solve inside the parentheses:
\[
3 + 5 = 8
\]
2. Multiply:
\[
5 \times 8 = 40
\]
3. Add:
\[
40 + 20 = 60
\]
Answer: \( 60 \)
---
Problem 2: \( 42 \div 7 + 9 \times 4 \)
1. Perform division and multiplication from left to right:
\[
42 \div 7 = 6
\]
\[
9 \times 4 = 36
\]
2. Add:
\[
6 + 36 = 42
\]
Answer: \( 42 \)
---
Problem 3: \( 20 + 4^2 \times 2 \)
1. Solve the exponent:
\[
4^2 = 16
\]
2. Multiply:
\[
16 \times 2 = 32
\]
3. Add:
\[
20 + 32 = 52
\]
Answer: \( 52 \)
---
Problem 4: \( 5^2 + 3^2 \times 2 \)
1. Solve the exponents:
\[
5^2 = 25
\]
\[
3^2 = 9
\]
2. Multiply:
\[
9 \times 2 = 18
\]
3. Add:
\[
25 + 18 = 43
\]
Answer: \( 43 \)
---
Problem 5: \( 12(32 \div 4) + 4^2 \)
1. Solve inside the parentheses:
\[
32 \div 4 = 8
\]
2. Multiply:
\[
12 \times 8 = 96
\]
3. Solve the exponent:
\[
4^2 = 16
\]
4. Add:
\[
96 + 16 = 112
\]
Answer: \( 112 \)
---
Problem 6: \( 4 \times 4 + 12 \times 7 \)
1. Perform multiplications:
\[
4 \times 4 = 16
\]
\[
12 \times 7 = 84
\]
2. Add:
\[
16 + 84 = 100
\]
Answer: \( 100 \)
---
Problem 7: \( 10(4 \times 5) \times 2 \)
1. Solve inside the parentheses:
\[
4 \times 5 = 20
\]
2. Multiply:
\[
10 \times 20 = 200
\]
\[
200 \times 2 = 400
\]
Answer: \( 400 \)
---
Problem 8: \( 5^2 \times 3(10 \div 5) \)
1. Solve the exponent:
\[
5^2 = 25
\]
2. Solve inside the parentheses:
\[
10 \div 5 = 2
\]
3. Multiply:
\[
3 \times 2 = 6
\]
\[
25 \times 6 = 150
\]
Answer: \( 150 \)
---
Problem 9: \( 96 \div 12(20 - 8) \times 2 \)
1. Solve inside the parentheses:
\[
20 - 8 = 12
\]
2. Perform division and multiplication from left to right:
\[
96 \div 12 = 8
\]
\[
8 \times 12 = 96
\]
\[
96 \times 2 = 192
\]
Answer: \( 192 \)
---
Problem 10: \( 22 \times 2 + 18 \times 2 \)
1. Perform multiplications:
\[
22 \times 2 = 44
\]
\[
18 \times 2 = 36
\]
2. Add:
\[
44 + 36 = 80
\]
Answer: \( 80 \)
---
Final Answers:
\[
\boxed{
\begin{aligned}
1. & \ 60 \\
2. & \ 42 \\
3. & \ 52 \\
4. & \ 43 \\
5. & \ 112 \\
6. & \ 100 \\
7. & \ 400 \\
8. & \ 150 \\
9. & \ 192 \\
10. & \ 80
\end{aligned}
}
\]
Parent Tip: Review the logic above to help your child master the concept of order of operations printable worksheet.
