Order of Operations Practice Problems with answers

Order of operations is a set of rules that dictate the correct sequence to evaluate a mathematical expression. The order of operations can be remembered using the acronym BODMAS or PEMDAS:

Solved Examples

Question 1: Solve 7 + 24 ÷ 8 × 4 + 6.

To solve 7 + 24 ÷ 8 × 4 + 6, we follow the PEMDAS rule,

First of all, we calculate 24 ÷ 8.

= 7 + 3 × 4 + 6

After this, we calculate 3 × 4,

= 7 + 12 + 6

Now, we perform the addition

= 25

So, 7 + 24 ÷ 8 × 4 + 6 = 25

Question 2: Evaluate 5 + 2 × 3²

First, we calculate the exponent:

3² = 9.

Then, we perform the multiplication:

2 × 9 = 18.

Finally, we add:

5 + 18 = 23.

So, 5 + 2 × 3² = 23.

Question 3: Simplify 15 − (6 + 3) × 4

First, we perform the operation inside the parentheses:

6 + 3 = 9.

Then, we multiply by 4:

9 × 4 = 36.

Finally, we subtract:

15 − 36 = −21.

So, 15 − (6 + 3) × 4 = −21.

Question 4: Evaluate: 12 − 3 × (4 − 1)

First, we calculate what's inside the parentheses:

4 − 1 = 3.

Then, we multiply:

3 × 3 = 9.

Finally, we subtract:

12 − 9 = 3.

So, 12 − 3 × (4 − 1) = 3.

Question 5: Solve: (10 − 3) × (2² + 1)

First, we calculate what's inside the parentheses:

10 − 3 = 7.

Then, we evaluate the exponent:

2² = 4.

Next, we add:

4 + 1 = 5.

Finally, we multiply:

7 × 5 = 35.

So, (10 − 3) × (2² + 1) = 35.

Question 6: Simplify: 20 ÷ (5 − 2) × 2

First, we calculate what's inside the parentheses:

5 − 2 = 3.

Then, we divide:

20 ÷ 3 = 20/3

Finally, we multiply:

20/3 × 2

So, 20 ÷ (5 − 2) × 2 = 40/3

Question 7: Evaluate: (8 ÷ 2) × (3 + 2)²

First, let's calculate what's inside the parentheses:

3 + 2 = 5.

Next, let's evaluate the exponent:

5² = 25

Then, let's calculate the division:

8 ÷ 2 = 4.

Finally, let's multiply:

4 × 25 = 100.

So, (8 ÷ 2) × (3 + 2)² = 100.

Question 8: Solve: 5 + 2 × (4 − 1)²

First, let's calculate what's inside the parentheses:

4 − 1 = 3.

Next, let's evaluate the exponent:

3² = 9.

Then, let's multiply:

2 × 9 = 18.

Finally, let's add:

5 + 18 = 23.

So, 5 + 2 × (4 − 1)² = 23.

Question 9: Simplify: 16 ÷ (4 − 1) + 2

First, let's calculate what's inside the parentheses:

4 − 1 = 3.

Next, let's perform the division:

16 ÷ 3 = 16/3 .

Then, let's add:

16/3 + 2

So, 16 ÷ (4 − 1) + 2 = 22/3.

Question 10: Evaluate: 3 + 4 × (6 − 3)²

First, let's calculate what's inside the parentheses:

6 − 3 = 3.

Next, let's evaluate the exponent:

3² = 9.

Then, let's multiply:

4 × 9 = 36.

Finally, let's add:

3 + 36 = 39.

So, 3 + 4 × (6 − 3)² = 39.

Practice Problems

Q1: Solve: 4 + 6 × (9 − 6)²

Q2: Simplify: (9+1)² ÷ (6 × 3)

Q3: Evaluate: 18 − 4 × (7 − 3)

Q4: Solve: (11 − 5) × (3² + 2)

Q5: Simplify: 24 ÷ (8 − 4) × 3

Q6: Evaluate: (10 ÷ 2) × (4 + 2)²

Q7: Evaluate: 6 + 5 × (8 − 4)²

Q8: Solve: (12 − 6) × (3 + 2)²

Q9: Simplify: 20 ÷ (7 − 4) + 3