People have come up with a common set of basic rules for performing computations.

Many years back, mathematicians came up with the standard “Order of Operations.” This is telling you which calculations should be made first in expressions that have more than just one operation.

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Without standard procedures for carrying out calculations, different people might get different answers when solving the same problem.

**This lesson is provided by Onsego GED Prep.**

**Next lesson:**What Are Integers, Prime Numbers, and Rational Numbers.

This lesson is a part of our GED Math Study Guide.

### Video Transcription

We explained parentheses earlier.

You must do the math part inside of the **parentheses first**.

When you’ve got ready with all of the stuff inside, you can move on to the operations that are in the problem’s open areas. Also, when they’re located inside the parentheses, you first need to complete the operations of** multiplication and division.**

When the problem to solve is “3 + 5 x 6”, you need to do the part “5 x 6” of the problem first and add the three (3) later to the product.

The same principle is true for divisions. A problem like, for example, “16 – 4 ÷ 2” needs to be done in two steps. First comes division, which results in the answer of 2. In the next step, you will subtract 2 from 16.

And when you have to deal with a variety of operations, addition and subtraction are the last steps.

So, begin with the parentheses, then move on to multiplication and division, and lastly, do addition and subtraction.

Here’s an example:

6 ÷ 2 x 5 – 5 + (11 – 3) = ?

1: Parentheses first: 6 : 2 x 5 – 5+ (8) = ?

2: Multiplication and Division:

In which order you need to be computing, multiplication, and division are always determined by which of the two comes first (from left to right).

6 ÷ 2 x 5 – 5+ (8) = ?

3 x 5 – 5 +(8) = ?

15 – 5 + 8=

3: Addition and Subtraction:

The order in which addition and subtraction must be dealt with first is determined by which one comes first as well (from left to right).

15-5+8=

10+8=18

**Order of Operations Summary**

1) First, carry out all operations within our grouping symbols. Grouping symbols include parentheses ( ), brackets [ ], braces { }, and fraction bars.

2) Then multiply and divide (always from left to right).

3) Then, add and subtract (from left to right).

**Summary**

The order in which we evaluate expressions can be ambiguous. The best way for avoiding ambiguities when evaluating expressions is establishing the correct order in which our operations must be performed. That’s crucial!

The guidelines described here should be strictly enforced at all times when we evaluate expressions.

*Last Updated on February 14, 2024.*