Let's solve each expression step by step, following the
order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right).
---
1. $ 8 + 4 - 3 = $
- Perform addition and subtraction from left to right:
$$
8 + 4 = 12 \\
12 - 3 = 9
$$
✔ Answer: 9
---
2. $ 38 - 19 + 12 = $
- Left to right:
$$
38 - 19 = 19 \\
19 + 12 = 31
$$
✔ Answer: 31
---
3. $ 7 + 9 \times (3 + 8) = $
- First, parentheses:
$$
3 + 8 = 11
$$
- Then multiplication:
$$
9 \times 11 = 99
$$
- Then addition:
$$
7 + 99 = 106
$$
✔ Answer: 106
---
4. $ 15 - 2^3 \div 4 = $
- First, exponent:
$$
2^3 = 8
$$
- Then division:
$$
8 \div 4 = 2
$$
- Then subtraction:
$$
15 - 2 = 13
$$
✔ Answer: 13
---
5. $ 55 \div 11 + 7 \times (2 + 14) = $
- Parentheses:
$$
2 + 14 = 16
$$
- Division and multiplication (left to right):
$$
55 \div 11 = 5 \\
7 \times 16 = 112
$$
- Then addition:
$$
5 + 112 = 117
$$
✔ Answer: 117
---
6. $ 5^3 - 12 \div 3 = $
- Exponent:
$$
5^3 = 125
$$
- Division:
$$
12 \div 3 = 4
$$
- Subtraction:
$$
125 - 4 = 121
$$
✔ Answer: 121
---
7. $ 8 \times (2^4 - 3) + 8 = $
- Exponent:
$$
2^4 = 16
$$
- Parentheses:
$$
16 - 3 = 13
$$
- Multiplication:
$$
8 \times 13 = 104
$$
- Addition:
$$
104 + 8 = 112
$$
✔ Answer: 112
---
8. $ 9 + 4^3 \times (20 - 8) \div 2 + 6 = $
- Parentheses:
$$
20 - 8 = 12
$$
- Exponent:
$$
4^3 = 64
$$
- Now expression becomes:
$$
9 + 64 \times 12 \div 2 + 6
$$
- Multiplication and division from left to right:
$$
64 \times 12 = 768 \\
768 \div 2 = 384
$$
- Now:
$$
9 + 384 + 6 = 400 - 1? Wait:
$$
9 + 384 = 393 \\
393 + 6 = 399
$$
✔ Answer: 399
---
✔ Final Answers:
1.
9
2.
31
3.
106
4.
13
5.
117
6.
121
7.
112
8.
399
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Parent Tip: Review the logic above to help your child master the concept of numerical expressions worksheet 5th grade.
