To solve the given problems, we will use the
BODMAS rule, which stands for:
-
B: Brackets
-
O: Orders (exponents and roots)
-
D: Division
-
M: Multiplication
-
A: Addition
-
S: Subtraction
We will solve each expression step by step.
---
1. \( 8 + 3 \times 2 = \)
-
Step 1: According to BODMAS, perform multiplication before addition.
\[
3 \times 2 = 6
\]
-
Step 2: Now add:
\[
8 + 6 = 14
\]
Answer: \( 14 \)
---
2. \( 10 - 6 \div 2 = \)
-
Step 1: According to BODMAS, perform division before subtraction.
\[
6 \div 2 = 3
\]
-
Step 2: Now subtract:
\[
10 - 3 = 7
\]
Answer: \( 7 \)
---
3. \( (6 + 2) \div 4 = \)
-
Step 1: Solve the expression inside the brackets first.
\[
6 + 2 = 8
\]
-
Step 2: Now perform the division:
\[
8 \div 4 = 2
\]
Answer: \( 2 \)
---
4. \( (8 + 1) \times (2 + 3) = \)
-
Step 1: Solve the expressions inside both brackets.
\[
8 + 1 = 9 \quad \text{and} \quad 2 + 3 = 5
\]
-
Step 2: Now multiply the results:
\[
9 \times 5 = 45
\]
Answer: \( 45 \)
---
5. \( 15 - 3^2 + 4 = \)
-
Step 1: According to BODMAS, calculate the exponent first.
\[
3^2 = 9
\]
-
Step 2: Substitute back and perform subtraction and addition from left to right.
\[
15 - 9 + 4 = 6 + 4 = 10
\]
Answer: \( 10 \)
---
6. \( 2 + 3 \times (3 + 2) = \)
-
Step 1: Solve the expression inside the brackets.
\[
3 + 2 = 5
\]
-
Step 2: Perform the multiplication.
\[
3 \times 5 = 15
\]
-
Step 3: Now add:
\[
2 + 15 = 17
\]
Answer: \( 17 \)
---
7. \( 8 + 4^2 \div 2 = \)
-
Step 1: Calculate the exponent.
\[
4^2 = 16
\]
-
Step 2: Perform the division.
\[
16 \div 2 = 8
\]
-
Step 3: Now add:
\[
8 + 8 = 16
\]
Answer: \( 16 \)
---
8. \( 20 - 8 - 3 \times (9 - 7) = \)
-
Step 1: Solve the expression inside the brackets.
\[
9 - 7 = 2
\]
-
Step 2: Perform the multiplication.
\[
3 \times 2 = 6
\]
-
Step 3: Substitute back and perform subtraction from left to right.
\[
20 - 8 - 6 = 12 - 6 = 6
\]
Answer: \( 6 \)
---
9. \( 2^2 + 6^2 - 4^2 = \)
-
Step 1: Calculate all the exponents.
\[
2^2 = 4, \quad 6^2 = 36, \quad 4^2 = 16
\]
-
Step 2: Substitute back and perform addition and subtraction from left to right.
\[
4 + 36 - 16 = 40 - 16 = 24
\]
Answer: \( 24 \)
---
10. \( (12 - 7) \times (3^2 - 2^2) = \)
-
Step 1: Solve the expressions inside both brackets.
\[
12 - 7 = 5
\]
\[
3^2 = 9 \quad \text{and} \quad 2^2 = 4 \quad \Rightarrow \quad 3^2 - 2^2 = 9 - 4 = 5
\]
-
Step 2: Now multiply the results:
\[
5 \times 5 = 25
\]
Answer: \( 25 \)
---
Final Answers:
\[
\boxed{14, 7, 2, 45, 10, 17, 16, 6, 24, 25}
\]
Parent Tip: Review the logic above to help your child master the concept of bodmas worksheet.
