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. Following this sequence ensures that everyone solves the expression the same way and gets the same result. The order of operations can be remembered using the acronym PEMDAS, which stands for:

• Parentheses
• Exponents
• Multiplication and Division
• Addition and Subtraction

PEMDAS and BODMAS are acronyms used to remember the order of operations in mathematics. BODMAS is similar but is commonly used in the United Kingdom and some other countries. It stands for:

• Brackets
• Orders (Exponents)
• Division and Multiplication (from left to right)
• Addition and Subtraction (from left to right)

Both PEMDAS or BODMAS are mnemonic devices to help remember the order in which mathematical operations should be performed when solving expressions or equations

Q1: Solve 7 + 24 ÷ 8 × 4 + 6.

Solution:

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

Q2: Evaluate 5 + 2 × 3²

Solution:

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.

Q3: Simplify 15 − (6 + 3) × 4:

Solution:

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.

Q4: Evaluate: 12 − 3 × (4 − 1)

Solution:

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.

Q5: Solve: (10 − 3) × (2² + 1)

Solution:

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.

Q6: Simplify: 20 ÷ (5 − 2) × 2

Solution:

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

Q7: Evaluate: (8 ÷ 2) × (3 + 2)²

Solution:

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.

Q8: Solve: 5 + 2 × (4 − 1)²

Solution:

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.

Q9: Simplify: 16 ÷ (4 − 1) + 2

Solution:

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.

Q10: Evaluate: 3 + 4 × (6 − 3)²

Solution:

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.

Q1: Evaluate: 7 + 3 × (5 − 2)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

Q10: Solve: 4 + 6 × (9 − 6)²