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Arithmetic Operations and PEMDAS in Mathematics

**Arithmetic operations and PEMDAS**
You will find several arithmetic problems on the GRE, GMAT or SAT, which involve intense calculations and if they are not done in a specific order, they can produce varying results. Because only one answer choice can be correct, you will not be rewarded for any other result except THE ONE. This requires mustering the ancient fundamentals that you might have leant at your schools level. The order of operations is a set of rules that tells us
how to evaluate expressions. You might have heard or used this acronym quite often, *PEMDAS.* Many also use a sentence to remember it “*Please Excuse My Dear Aunt Sally.” *
Whichever way you choose, what is quintessential is to remember the way in which arithmetic operations follow* PEMDAS.*
The letters in **PEMDAS **are meant to help you remember to:
- Simplify expressions inside
**P**arentheses.
- Evaluate powers, or numbers with
**E**xponents.
**M**ultiply and **D**ivide, moving from left to right.
**A**dd and **S**ubtract, moving from left to right.

Multiplication and division have the same priority. Do multiplications or division as you meet them as you work across the line, rather than doing all the multiplication and then all the division. The same is true for addition and subtraction. Do them as you come to them. Do not give addition a higher rank than subtraction.
**EXAMPLE:**
**Find the simplest value for 8 × [2 × (4 + 3)2 – 20 + 12] ÷ 4.**
Grouping symbols take precedence. So, working from the inside out:
8 × [2 × (4 + 3)^^{2} – 20 + 12] ÷ 4 Add 4 + 3.
8 × [2 × (7)^^{2} – 20 + 12] ÷ 4 Square 7.
8 × [2 × 49 – 20 + 12] ÷ 4 Multiply 2 × 49.
8 × [98 – 20 + 12] ÷ 4 Subtract 98 – 20.
8 × [78 + 12] ÷ 4 Add 78 + 12.
8 × [90] ÷ 4 Multiply 8 × 90.
720 ÷ 4 Divide 720 ÷ 4.
180
You get the answer: 180.
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