To solve the given numerical expressions, we need to follow the
order of operations, often remembered by the acronym
PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).
Let's solve each expression step by step:
---
(a) \( 3 \times 2 + 8 - 5 \)
1. Perform multiplication first:
\[
3 \times 2 = 6
\]
So the expression becomes:
\[
6 + 8 - 5
\]
2. Perform addition and subtraction from left to right:
\[
6 + 8 = 14
\]
\[
14 - 5 = 9
\]
Answer:
\[
\boxed{9}
\]
---
(b) \( 18 + 4 \times 6 \div 2 - 9 \)
1. Perform multiplication and division from left to right:
\[
4 \times 6 = 24
\]
So the expression becomes:
\[
18 + 24 \div 2 - 9
\]
Next, perform the division:
\[
24 \div 2 = 12
\]
So the expression becomes:
\[
18 + 12 - 9
\]
2. Perform addition and subtraction from left to right:
\[
18 + 12 = 30
\]
\[
30 - 9 = 21
\]
Answer:
\[
\boxed{21}
\]
---
(c) \( 14 + 28 \div 7 \times 3 - 17 \)
1. Perform division and multiplication from left to right:
\[
28 \div 7 = 4
\]
So the expression becomes:
\[
14 + 4 \times 3 - 17
\]
Next, perform the multiplication:
\[
4 \times 3 = 12
\]
So the expression becomes:
\[
14 + 12 - 17
\]
2. Perform addition and subtraction from left to right:
\[
14 + 12 = 26
\]
\[
26 - 17 = 9
\]
Answer:
\[
\boxed{9}
\]
---
(d) \( 18 - 2 \times 10 \div 2 + 2 \)
1. Perform multiplication and division from left to right:
\[
2 \times 10 = 20
\]
So the expression becomes:
\[
18 - 20 \div 2 + 2
\]
Next, perform the division:
\[
20 \div 2 = 10
\]
So the expression becomes:
\[
18 - 10 + 2
\]
2. Perform subtraction and addition from left to right:
\[
18 - 10 = 8
\]
\[
8 + 2 = 10
\]
Answer:
\[
\boxed{10}
\]
---
(e) \( 25 \div 5 \times 8 + 6 - 12 \)
1. Perform division and multiplication from left to right:
\[
25 \div 5 = 5
\]
So the expression becomes:
\[
5 \times 8 + 6 - 12
\]
Next, perform the multiplication:
\[
5 \times 8 = 40
\]
So the expression becomes:
\[
40 + 6 - 12
\]
2. Perform addition and subtraction from left to right:
\[
40 + 6 = 46
\]
\[
46 - 12 = 34
\]
Answer:
\[
\boxed{34}
\]
---
(f) \( 27 - 9 + 4 \times 5 \)
1. Perform multiplication first:
\[
4 \times 5 = 20
\]
So the expression becomes:
\[
27 - 9 + 20
\]
2. Perform subtraction and addition from left to right:
\[
27 - 9 = 18
\]
\[
18 + 20 = 38
\]
Answer:
\[
\boxed{38}
\]
---
(g) \( 17 \times 3 + 81 \div 9 - 60 \)
1. Perform multiplication and division from left to right:
\[
17 \times 3 = 51
\]
So the expression becomes:
\[
51 + 81 \div 9 - 60
\]
Next, perform the division:
\[
81 \div 9 = 9
\]
So the expression becomes:
\[
51 + 9 - 60
\]
2. Perform addition and subtraction from left to right:
\[
51 + 9 = 60
\]
\[
60 - 60 = 0
\]
Answer:
\[
\boxed{0}
\]
---
(h) \( 27 - 42 \div 3 + 16 \)
1. Perform division first:
\[
42 \div 3 = 14
\]
So the expression becomes:
\[
27 - 14 + 16
\]
2. Perform subtraction and addition from left to right:
\[
27 - 14 = 13
\]
\[
13 + 16 = 29
\]
Answer:
\[
\boxed{29}
\]
---
Final Answers:
\[
\boxed{9, 21, 9, 10, 34, 38, 0, 29}
\]
Parent Tip: Review the logic above to help your child master the concept of simplify numerical expressions worksheet.
