Person A may think, "I'll do 6 + 7 first, then multiply it to 5". The results are, however,

6 + 7 × 5

= 13 × 5

= 65

Person B may think, "I'll multiply 7 by 5 first, then add the result to 6". This results in the

6 + 7 × 5

= 6 + 35

= 41

While there are many ways to solve one particular math or algebra problem, the following order of operations must be followed in Arithmetic AND Algebra to get the correct result. The list is from the most important to the least important.

You can remember this as

Here are some examples to help you understand how the order of operations list is used. To be sure you've understood all the concepts, make sure that you've at least understood Example 6.

This is a variation of the earlier example.

Evaluate (6 + 7) × 5.

In this case, be sure to evaluate the bracketed values first, since it's on top of the list. Evaluate them from left to right, i.e. (6 + 4) followed by (5 + 3). After that, evaluate the multiplication operation.

(6 + 4) × (5 + 3)

= 10 × 8

= 80

So the rule here is, parenthesis is king, and evaluate them from left to right.

In this example, we have the nested parenthesis (7 + 7). Evaluate the most nested parenthesis first (it has no more nested parenthesis in it). Then evaluate the other parentheses from left to right.

(6 + 5) × (3 × (7 + 3))

= (6 + 5) × (3 × 10)

= 11 × 30

= 330

Typically exponents are grouped together by parenthesis. Note that exponents are at the same level as roots.

In this case, multiplication and division is at the same level, so it must be evaluated from left to right.

6 × 10 ÷ 2 × 3

= 60 ÷ 2 × 3

= 30 × 3

= 90

Addition and subtraction are at the same level. You can evaluate any pair of addition and subtraction, but it's preferable to systematically evaluate it from left to right.

6 + 7 – 3 + 5

= 13 – 3 + 5

= 10 + 5

= 15

6 + 7 – 3 + 5

= 6 + 4 + 5

= 15

6 + 7 – 3 + 5

= 13 + 2 (because -3 + 5 = 2)

= 15

The following order of operations example may seem complicated, but it's really easy to solve if you approach it systematically. We typically solve for the top and bottom of the fraction separately (also known as the numerator and denominator, respectively). For convenience, in the first step I chose to solve the inner most bracket of the top of the fraction, that is, (-3)

In the following step, we need to expand -2

Now we turn our attention to the denominator. Using PEMDAS, we find that multiplication has a higher priority than addition, so 4 × 3 is evaluated first. The rest of the steps are self-explanatory, so I won't be explaining them here.

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