# BODMAS/PEMDAS Rules – Involving Decimals | Order of Operations with Decimals Questions and Answers

We can easily simplify the arithmetic expression which involves decimals by using the BODMAS Rules or PEMDAS Rules. Some children will get confused while simplifying an arithmetic expression but by using the BODMAS rule, they can simply solve the expressions. Check out the Order of Operations and solved examples of BODMAS Rules Involving Decimals in this article. We have clearly given questions and answers along with the explanations for your best practice.

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## Order of Operations Involving Decimals Questions and Answers

Example 1.

First priority for Bracket terms: Solve inside the Brackets/parenthesis before Of, Multiply, Divide, Add or Subtract.
For example 1.2 + (1.5 – 2.3).

Solution:

The given expression is 1.2 + (1.5 – 2.3).
1.2 + (1.5 – 2.3) = 1.2 + (- 0.8) (subtraction of bracket term).
= 1.2 – 0.8.
= 0.4.
Finally, 1.2 + (1. 5 – 2. 3) is equal to 0.4.

Example 2.

Order terms are second priority: Then, solve Of part (Exponent, Powers, Roots, etc.,) before Multiply, Divide, Add or Subtract.
For example 0.2 X (1.2 + 1.4) + (0.2)^2.
Solution:

The given expression is 0.2 X (1.2 + 1.4) + (0.2)^2.
0.2 X (1.2 + 1.4) + (0.2)^2 = 0.2 X 2.6 + (0.2)^2 ( bracket terms addition first).
= 0.2 X 2.6 + 0.04 (order term (0.2)^2 = 0.04).
= 0.52 + 0.04 (multiplication 0.2 X 2.6 = 0.52).
= 0.56 (addition 0.52 + 0.04 = 0.56).
Therefore, 0.2 X (1.2 + 1.4) + (0.2)^2 is equal to 0.56.

Example 3.

Division and Multiplication: Then, calculate Multiply or Divide before Add or Subtract start from left to right.
For example 1.4 + 1.6 ÷ 0.2 X 0.2.
Solution:

The given expression is1.4 + 1.6 ÷ 0.2 X 0.2.
1.4 + 1.6 ÷ 0.2 X 0.2 = 1.4 + 8 X 0.2 (division 1.6 ÷ 0.2 = 8).
= 1.4 + 0.4 (multiplication 8 X 0.2 = 0.4).
= 1.8 (addition 1.4 + 0.4 = 1.8).
Therefore, 1.4 + 1.6 ÷ 0.2 X 0.2 is equal to 1.8.

Example 4.

Addition and Subtraction: At last Add or Subtract start from left to right.
For example 1.5 + (3.2 – 1.6) + 0.1.
Solution:

The given expression is 1.5 + (3.2 – 1.6) + 0.1.
1.5 + (3.2 – 1.6) + 0.1 = 1.5 + 1.6 + 0.1 (subtraction of bracket terms 3.2 – 1.6 = 1.6).
= 3.2 (addition 1.5 + 1.6 + 0.1 = 3.2).
Therefore, 1.5 + (3.2 – 1.6) + 0.1 is equal to 3.2.

### BODMAS Rules Involving Decimals Questions and Answers

Problem 1.

Simplify the below expressions by using the BODMAS rules.
(i) 0.4 + 0.8 ÷ 0.2 + 0.2 X 0.4.
(ii) 0.2 X 0.5(1.2 + 2.1) + 2.5.
(iii) 0.6 – 0.2 X 1.2 + 1.6.
(iv) 1.2 + [2.5 + (2.6 – 1.6) – 2.4)] – 3.2.
(v) 0.8 + 1.2 X 0.5 + 1.2.

Solution:

(i) 0.4 + 0.8 ÷ 0.2 + 0.2 X 0.4.
Solution:
The given expression is 0.4 + 0.8 ÷ 0.2 + 0.2 X 0.4.
0.4 + 0.8 ÷ 0.2 + 0.2 X 0.4 = 0.4 + 4 + 0.2 X 0.4 (division 0.8 ÷ 0.2 = 4).
= 0.4 + 4 + 0.08 (multiplication 0.2 X 0.4 = 0.08).
= 4.48.
By using the BODMAS Rule, 0.4 + 0.8 ÷ 0.2 + 0.2 X 0.4 is equal to 4.48.

(ii) 0.2 X 0.5(1.2 + 2.1) + 2.5.
Solution:
The given expression is 0.2 X 0.5(1.2 + 2.1) + 2.5.
0.2 X 0.5(1.2 + 2.1) + 2.5 = 0.2 X 0.5(3.3) + 2.5 (addition 1.2 + 2.1 = 3.3).
= 0.2 X 0.5 X 3.3 + 2.5
= 0.33 + 2.5 (multiplication 0.2 X 0.5 X 3.3 = 0.33).
= 2.83 (addition 0.33 + 2.5 = 4.83).
By using the BODMAS rule, the given expression 0.2 X 0.5(1.2 + 2.1) + 2.5 is simplified as 2.83.

(iii) 0.6 – 0.2 X 1.2 + 1.6.
Solution:
The given expression is0.6 – 0.2 X 1.2 + 1.6.
0.6 – 0.2 X 1.2 + 1.6 = 0.6 – 0.24 + 1.6 (multiplication 0.2 X 1.2 = 0.24).
= 2.2 – 0.24 (addition 0.6 + 1.6 = 2.2).
= 1.96 (subtraction 2.2 – 0.24 = 1.96).
Finally, by using the BODMAS rule, the given expression 0.6 – 0.2 X 1.2 + 1.6 is simplified as 1.96.

(iv) 1.2 + [2.5 + (2.6 – 1.6) – 2.4)] – 3.2.
Solution:
The given expression is 1.2 + [2.5 + (2.6 – 1.6) – 2.4)] – 3.2.
1.2 + [2.5 + (2.6 – 1.6) – 2.4)] – 3.2 = 1.2 + [2.5 + (1.0) – 2.4)] – 3.2 (subtraction in brackets 2.6 – 1.6 = 1.0).
1.2 + [2.5 + (2.6 – 1.6) – 2.4)] – 3.2 = 1.2 + [3.5 – 2.4] – 3.2 (addition 2.5 + 1.0 = 3.5).
1.2 + [2.5 + (2.6 – 1.6) – 2.4)] – 3.2 = 1.2 + 1.1 – 3.2 (subtraction 3.5 – 2.4 = 1.1).
1.2 + [2.5 + (2.6 – 1.6) – 2.4)] – 3.2 = 2.3 – 3.2 (addition 1.2 + 1.1 = 2.3).
= – 0.9 (subtraction 2.3 – 3.2 = – 0.9).
By using the BODMAS rule, the given expression 1.2 + [2.5 + (2.6 – 1.6) – 2.4)] – 3.2 is simplified as – 0.9.

(v) 0.8 + 1.2 X 0.5 + 1.2.
Solution:
The given expression is 0.8 + 1.2 X 0.5 + 1.2.
0.8 + 1.2 X 0.5 + 1.2 = 0.8 + 0.6 + 1.2 (multiplication first 1.2 X 0.5 = 0.6).
= 2.6 (addition 0.8 + 0.6 + 1.2 = 1.4 + 1.2 = 2.6).
By using the BODMAS rule, 0.8 + 1.2 X 0.5 + 1.2 is simplified as 2.6.