We have multiple operations in one arithmetic expression. To simplify the expression very easily, we have to follow the PEMDAS rules. The PEMDAS rule is an order of operations. By using the PEMDAS Rule, we can know the priority levels of the operations in mathematics. So, we can easily simplify the arithmetic expressions involves integers. Check out the PEMDAS Rules applied to the integers and solving methods to find the answers.

Also, Read:

## How to do Order of Operations with Integers?

1. First priority for Parenthesis terms {}, (), [].

For example, 2 × (10+15).

2 × 25 (parenthesis term first).

50 (multiplication).

2. Second Priority for Exponent Terms a².

For example, 10 + (20 × 2) + 4².

10 + (20 × 2) + 4² = 10 + 40 + 4² (Parenthesis term 20 × 2 = 40).

= 10 + 40 + 16 (Exponent Term 4² = 16 second priority).

= 66 (addition).

3. Third Priority for Multiplication a × b.

For example, 25 × 2 + (10 + 2) + 2².

25 × 2 + 12 + 2² (Parenthesis first 10 +2 = 12).

25 × 2 + 12 + 4 (Exponent Second 2² = 4).

50 + 12 + 4 (Multiplication third 25 × 2 = 50).

66 (addition).

4. Fourth Priority for Division a ÷ b.

For example, 100 ÷ 2 × 25 + (20 × 2) + (10 + 2)².

100 ÷ 2 × 25 + 40 + 12² (Parenthesis first 20 × 2 = 40 and 10 + 2 = 12).

100 ÷ 2 × 25 + 40 + 144 (Exponent Second 12² = 144).

100 ÷ 50 + 40 + 144 (Multiplication Third 25 × 2 = 50).

2 + 40 + 144 (Division Fourth 100 ÷ 50 = 2).

186 (addition).

5. Next priority for Addition a + b.

For example, 14 × 2 ÷ 4 + (25 + 5) + 5².

14 × 2 ÷ 4 + 30 + 5² (Parenthesis First 25 + 5 = 30).

14 × 2 ÷ 4 + 30 + 25 (Exponent 5² = 25).

28 ÷ 4 + 30 + 25 (Multiplication Third 14 × 2 = 28).

7 + 30 + 25 (Division Fourth 28 ÷ 4 = 7).

62 (fifth priority for addition 7 + 30 + 25 = 62).

6. Next priority for Subtraction a – b.

For example, 10 × 2 + 15 ÷ 5 + (100 × 2) – 15 + 2².

10 × 2 + 15 ÷ 5 + 200 – 15 + 2² (Parenthesis First 100 × 2 = 200).

10 × 2 + 15 ÷ 5 + 200 – 15 + 4 (Exponent second priority 2² =4).

20 + 15 ÷ 5 + 200 – 15 + 4 (Multiplication Third 10 × 2 = 20).

20 + 3 + 200 – 15 + 4 (Division fourth priority 15 ÷ 5 = 3).

227 – 15 (Addition Fifth Priority 20 + 3+ 200 + 4 = 227).

212 (Subtraction 227 – 15 = 212).

### Solved Examples on How to Simplify PEMDAS Involving Integers

1. Simplify the given Expressions by using the PEMDAS Rule

(i) 10 – 24 ÷ 6 + 20 × (30 + 5).

(ii) 25 – [(15 × 2) + (30 +10)] + 5².

(iii) 62 + 25 of (50 – 20) × 25².

(iv) 40 + 25- 46 × 30 + (10 + 35).

(i) 10 – 24 ÷ 6 + 20 × (30 + 5).

Solution:

The given expression is 10 – 24 ÷ 6 + 20 × (30 + 5).

Based on the PEMDAS rule, we need to follow the order of operations. That is Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction.

10 – 24 ÷ 6 + 20 × (30 + 5).

Simplify the Parenthesis terms first. That is

10 – 24 ÷ 6 + 20 × 35.

Simplify the Multiplication Term. That is,

10 – 24 ÷ 6 + 700.

Simplify the Division Term. That is,

10 – 4 + 700.

Simplify the Addition term. That is,

710 – 4.

Simplify the subtraction. That is,

706.

Therefore, 10 – 24 ÷ 6 + 20 × (30 + 5) is equal to 706.

(ii) 25 – [(15 × 2) + (30 +10)] + 5².

Solution:

The given expression is25 – [(15 × 2) + (30 +10)] + 5².

As per the PEMDAS rule, the order of operations is Parenthesis, Exponent, Multiplication, Division, Addition, Subtraction.

25 – [(15 × 2) + (30 +10)] + 5².

25 – [30 + 40] + 5² (parenthesis term simplification).

25 – 70 + 5² (again parenthesis term simplification).

25 – 70 + 25 (Exponent term simplification).

50 – 70 (addition simplification).

-20 (subtraction).

Therefore, 25 – [(15 × 2) + (30 +10)] + 5² is equal to – 20.

(iii) 62 + 25 of (50 – 20) × 25².

Solution:

The given expression is 62 + 25 of (50 – 20) × 25².

As per the PEMDAS rule, the order of operations is Parenthesis, Exponent, Multiplication, Division, Addition, Subtraction.

62 + 25 of (50 – 20) × 25².

Solve the Parenthesis term. That is

62 + 25 of (30) × 25².

We can write it as 62 + 25 × 30 × 25².

Next, simplify the exponent terms. That is

62 + 25 × 30 × 625.

The next priority for simplification is multiplication. That is

62 + 4,68,750.

4,68,812.

Therefore, 62 + 25 of (50 – 20) × 25² is equal to 4,68,812.

(iv) 40 + 25- 46 × 30 + (10 + 35).

Solution:

The given expression is 40 + 25- 46 × 30 + (10 + 35).

As per the PEMDAS rule, the order of operations is Parenthesis, Exponent, Multiplication, Division, Addition, Subtraction.

40 + 25- 46 × 30 + (10 + 35).

We need to simplify the parenthesis terms first. That is

40 + 25- 46 × 30 + 45.

Next, simplify the multiplication terms. That is

40 + 25 – 1380 + 45.

Simplify the additional terms. That is

110 – 1380.

Subtract the above terms. That is

-1270.

Therefore, 40 + 25- 46 × 30 + (10 + 35) is equal to – 1270.