PEMDAS Step by Step

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These order of operations worksheets teach the way to figure equations in the correct order, step by step like shown in the Saxon Math books.

Remember that exponents come second in the order of operations for Pre-Algebra. This phrase makes it easy to remember that **PEMDAS Stands For:**

"Please excuse my dear Aunt Sara." or use the phrase PEMDAS for solving what is in the Parentheses first, the Exponents next, Multiplication and Division, and finally Addition and Subtraction - all from left to right.

Use this phrase to remember the order when using these worksheets:

*Exponents come second in the order of operations for Pre-Algebra. Use
this phrase to remember the order: "Please excuse my dear Aunt Sara." or
use the phrase PEMDAS. *

Memorize the PEMDAS line.

Parenthesis, exponents, multiplication, division, addition, and subtraction; but remember that in the real world multiplication and division are of equal priority as are addition and subtraction. These order of operations worksheets teach it this way because the math books do and it's easy to remember.

The phrase "**P**lease **e**xcuse **m**y **d**ear **A**unt
**S**ara." is cute and short. It works well with guided problem solving and you must use that
formula if your Math textbooks use it, because you'll get a wrong answer
if you don't. Memorization makes Math easier, so memorize that
operations of equal priority should be worked left to right - usually.
See what we found at Wikipedia below.

All my Algebraic life I've wondered what Wikipedia answers well:

*
"From the earliest use of mathematical notation multiplication took
precedence over addition, whichever side of a number it appeared. Thus 3
+ 4 × 5 = 4 × 5 + 3 = 23. When exponents were first introduced, in the
16th and 17th centuries, exponents took precedence over both addition
and multiplication, and could be placed only as a superscript to the
right of their base. Thus 3 + 5 2 = 28 and 3 × 5 2 = 75. To change the
order of operations, originally a vinculum (an overline or underline)
was used. Today we use parentheses. Thus, to force addition to precede
multiplication, write (2 + 3) × 4 = 20."*

Wikipedia points out that multiplication and division are of equal importance so that they can trade places. The same is true of addition and subtraction.

*"
These mnemonics may be misleading, especially if the user is not aware
that multiplication and division are of equal precedence, as are
addition and subtraction. Using any of the above rules in the order
"addition first, subtraction afterward" would give the wrong answer to
many equations."*

10 - 3 + 2 figured left to right is 9

If you figured the addition first the answer is 5. The order of operations really matters.

Further…

*The order of operations, or precedence, used in mathematics and many programming languages is expressed here:terms inside parentheses or bracketsexponents and rootsmultiplication and division As they appear left to rightaddition and subtraction As they appear left to right*

*This
means that if a mathematical expression is preceded by one operator and
followed by another, the operator higher on the list should be applied
first. The commutative and associative laws of addition and
multiplication allow terms to be added in any order and factors to be
multiplied in any order, but mixed operations must obey the standard
order of operations.*

*It is helpful to treat division as multiplication by the reciprocal (multiplicative inverse) and subtraction as addition of the opposite (additive inverse).
Thus 3/4 = 3 ÷ 4 = 3 • ¼; in other words the quotient of 3 and 4 equals
the product of 3 and ¼. Also 3 − 4 = 3 + (−4); in other words the
difference of 3 and 4 equals the sum of positive three and negative
four. With this understanding, we can think of 1 - 2 + 3 as the sum of
1, negative 2, and 3, and add in any order: (1 - 2) + 3 = -1 + 3 = 2 and
in reverse order (3 - 2) + 1 = 1 + 1 = 2. The important thing is to
keep the negative sign with the 2.*

The order of operations worksheets below reflect the left to right rule from Saxon's Math 7/6 page 495:

1. Simplify within **P**arentheses.

2. Simplify **E**xponential powers and roots.

3. **M**ultiply and **D**ivide from left to right.

4. **A**dd and **S**ubtract from left to right.

Thanks to Crewton Ramone and Teresa C for helping here!

I made these printable Math exponent worksheets and charts to offer the practice necessary to become fast using exponents.

If your kids are not familiar enough with multiplication and division to tackle exponents, we have multiplication and division worksheets that are pure practice.

Negative exponents mean the reciprocal of the base raised to the power of the exponent.

Thank you for visiting our Order of Operations worksheets.

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