Today we have a visiting contributor, Emma Mooreq. She has a great article to share with us. I have noticed as I had substitute teach in fourth grade classrooms they were not very familiar with this concept. While they might not be working with exponents, it is a very handy rule to know. I still remember it as ‘Please Excuse My Dear Aunt Sally’. Do you remember learning it that way? ~Lucy

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In algebra, the order of operations is frequently used to solve the mathematical expression in a
similar way all over the world by using the PEMDAS rule. This rule is used to avoid the wrong
way of calculations and solve the problems in a well-known order.
In this article, we’ll study how to solve the expressions of mathematics by using the PEMDAS
rule.

What is the PEMDAS rule?

In mathematics, the PEMDAS rule is a rule that expresses the accurate sequence of steps for solving a math expression.

PEMDAS stands for Parentheses, Exponents (power), Multiplication, Division, Addition, & Subtraction.

According to this rule, you have to solve the parentheses of the math expression first, then solve the exponents, after that multiplication & division from left to right, and in the last addition & subtraction from left to right. 

 If there is more than one similar operation then solve the leftmost operation first and then solve the next one. 

How to solve math expressions by using the PEMDAS rule?

The problems of math expressions can be solved easily either by using the PEMDAS rule or a PEMDAS calculator. Below is an example of a math expression solved by using the PEMDAS rule.

Example

Evaluate 24 x 5 – 142 + 25/5 – (19 + 12) + 3 x (1 + 2) by using the PEMDAS rule.

Solution 

Step 1: Write the given math expression.

24 x 5 – 142 + 25/5 – (19 + 12) + 3 x (1 + 2) 

Step 2: First of all, solve the parentheses of the given expression.

24 x 5 – 142 + 25/5 – (31) + 3 x (1 + 2) 

24 x 5 – 142 + 25/5 – 31 + 3 x (3) 

24 x 5 – 142 + 25/5 – 31 + 3 x 3 

Step 3: Solve the exponent terms of the expression.

24 x 5 – (14 x 14) + 25/5 – 31 + 3 x 3 

24 x 5 – 196 + 25/5 – 31 + 3 x 3 

Step 4: Now solve the multiplication & division operations from left to right.

120 – 196 + 25/5 – 31 + 3 x 3 

120 – 196 + 5 – 31 + 3 x 3 

120 – 196 + 5 – 31 + 9

Step 5: Solve the addition & subtraction operations from left to right.

– 76 + 5 – 31 + 9

– 71 – 31 + 9

– 102 + 9

-93

Hence,

24 x 5 – 142 + 25/5 – (19 + 12) + 3 x (1 + 2) = -93

Summary 

After reading the above article, you can solve any math expression in a correct sequence of steps. The order of operation is not a difficult topic, you have to follow the steps of the PEMDAS rule to find an accurate result.

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