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spacer math worksheets > > order of operations > > quick tips

SuperKids Math Review

How to Solve Order of Operations Problems

After learning to add and subtract, multiply and divide, students will encounter equations that combine these operations. For example:

4 + 3 x 5 = ?
Is the answer:
  (4 + 3) x 5   =   7 x 5   =   35?

or is it:
  4 + (3 x 5)   =   4 + 15   =   19?

Mathematicians have established a standard way to solve these types of problems, that defines the order in which we solve the different math operations in an equation. An easy way to remember the order is the acronym, PEMDAS.

Order of Operations = PEMDAS

Here's the trick you need to memorize:
P = Parentheses
E = Exponents
M = Multiplication and
D = Division
A = Addition and
S = Subtraction

Problems involving order of operations are answered by first solving anything within parentheses, then dealing with exponents, then multiplication and division (working from left to right), and finally addition and subtraction. And if there are parentheses within parentheses, we work from the inside out.

Let's look again at our sample problem:

4 + 3 x 5 = ?
Since there are no parentheses, and no exponents, we start by solving the multiplication (3 x 5), and add the result (15) to the remaining element (4), to get 4 + 15 = 19.

How about a trickier problem? Well, if you remember PEMDAS, there really are no tricky problems. Here's one that may look harder, but if we follow the PEMDAS order, the answer is easily found:

((4 + 3) x (5 - 2) + 7) 2 = ?

Start by solving the parts inside the parentheses:
(4 + 3) = 7 and (5 - 2) = 3
Then rewrite the equation:
(7 x 3 + 7) 2 = ?

Next do the multiplication inside the parentheses:
7 x 3 = 21
And again rewrite the equation:
(21 + 7) 2 = ?

Still inside the parentheses, do the addition:
21 + 7 = 28
Rewrite the equation one last time:
28 2 = ?
And finally perform the division to get the answer:
28 2 = 14

No tricks, just remember PEMDAS!



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