Order of Operations - PEMDAS

Order of Operations - PEMDAS

*When evaluating an expression, follow this order to complete the simplification:

Parenthesis ? "( )" EX. (5-2)+3=6

(5 minus 2 must be done before adding 3 because it is in parenthesis.)

Exponents ? "32 " EX. 32(4)=36

(32 must be done before multiplying by 4 because exponents come before multiplying.)

Multiplication ? "x,." EX. 3x2-5=1

(3 times 2 must be done before subtracting 5 because multiplying comes before subtraction.)

Division - EX. 4/2-1=1

(4 divided by 2 must be done before subtracting 1 because division comes before subtraction.)

Addition ? "+" EX. 5+2-3=0

(5 plus 2 must be done before subtracting 3 because addition comes before subtraction.)

Subtraction ? "-" is done last

Rules for Multiplying or Dividing Positive/Negative Numbers

*When multiplying or dividing, if the signs of the integers (numbers) are the same, the answer will ALWAYS be positive.

EXAMPLE

+, + "+" +8(+3)=+24...(Positive 8 times positive 3 equals positive 24)

-, -

-5 x -6=30...(Negative 5 times negative 6 equals positive 30)

+6/+2=+3...(Positive 6 divided by positive 2 equals positive 3)

-8/-4=+2...(Negative 8 divided by negative 4 equals positive 2)

*When multiplying or dividing, if the signs of the integers (numbers) are different, the answer will ALWAYS be negative.

EXAMPLE

+,-

-3(3)=-9...(Negative 3 times positive 3 equals negative 9)

-,+ "-" 4 x (-2)=-8...(Positive 4 times negative 2 equals negative 8)

-12/+4=-3...(Negative 12 divided by positive 4 equals negative 3)

+9/-3=-3...(Positive 9 divided by negative 3 equals negative 3)

Rules for Adding/Subtracting Positive/Negative Numbers

*If the signs of the integers (numbers) are the same, then add the numbers and keep the same sign.

EXAMPLE

3+4=+7...(A positive plus a positive gives us a larger positive) -7-2=-9...(A negative and another negative gives us a larger negative)

*If the signs of the integers (numbers) are different, then subtract the numbers and keep the sign of the larger number.

EXAMPLE

+8-3=+5...(Subtract 8 minus 3 to get 5, then keep the sign of the larger number (8), which is positive) -7+5=-2...(Subtract 7 minus 5 to get 2, then keep the sign of the larger number (7), which is negative)

ADDING AND SUBTRACTING FRACTIONS

* In order to add or subtract fractions, you must first find the LCD (Lowest Common Denominator). Top number is always the numerator, bottom always the denominator.

Example

1 2 5 5

6 2 (6 and 2 are numerators) 7 7 (both 7's are denominators)

* When adding or subtracting fractions with given common denominators, just add or subtract the numerators (top numbers). The denominators will not change.

1 5

2 5

=

3 5

final answer

6 7

2 7

=

4 7

final answer

* If you are asked to add or subtract fractions which do not have a given common denominator, we must use multiples of each denominator to find the LCD (Lowest Common Denominator).

3 5 4 8

5 1 15 5

multiples of 4: 4, 8, 12, 16 multiples of 8: 8, 16, 24

multiples of 5: 5, 10, 15, 20 multiples of 15: 15, 30, 45

Which is the lowest common number in both lines? ~ 8 is the lowest common denominator for 4 and 8. ~ 15 is the lowest common denominator for 5 and 15.

* In order to create common denominators, one or more numbers might need to be multiplied. Whatever is multiplied for the denominator must be multiplied to the numerator. For example:

3.2 5.1

6 5

4.2 8.1 becomes 8 8

5.1 1.3

5 3

15.1 5.3 becomes 15 15

*Now, just add or subtract the numerators.

6 5 11 final answer

8

8

= 8

5 3 2 final answer =

15 15 15

MULTIPLYING FRACTIONS

* When multiplying fractions, simply multiply numerator times numerator and denominator times denominator.

Example

2 3 6 x =

3 4 12

5 4 20 ? =

2 7 14

* Now see if the fraction in your answer can be reduced.

6 ?6

?

12 ?? 6

1 final answer 2

20

? ?

2

?

14 ? 2

10 final answer 7

DIVIDING FRACTIONS

* When dividing fractions, you must first change the division sign to multiplication. Then you must flip the dividend (2nd number in the problem) upside down. For example:

4? 2 ?

5 3

becomes

1 ? 3 ?

5 4

4 5

x

3 2

* Now, just multiply.

1 5

x

4 3

4 5

x

3 2

=

12 10

1 5

?

4 3

=

4 15

* Now see if the fraction in your answer can be reduced.

12

? ?

2

10

? ?

2

6 final answer 5

4 final answer 15

ADDING AND SUBTRACTING DECIMALS

* When adding or subtracting decimals, decimals points must line up. Then add or subtract and drop the decimal straight down.

Example

.23 +2.51

2.74

4.13 -2.02 2.11

231.46 +25.3 256.76

24.2 - 1.6 24.04

MULTIPLYING DECIMALS

* When multiplying decimals, first multiply the numbers as if the decimals don't exist.

Example

.3

x.2

6

5.4 x.23 162 +1080 1242

* Next, count up the amount of numbers that are to the right of any decimal points.

.3 2 numbers to x.2 the right of the decimal

6 (3 and 2)

* Place your decimal at the end of the answer.

5.4 x.23 162 +1080 1242

3 numbers to to the right of the decimal (4, 3, and 2)

.3 x.2

6.

* Now, move the decimal to the left.

.3 (2 times) x.2 .06. final answer

.06

5.4 x.23

162 +1080

1242.

5.4 x.23

162 +1080

12. 42.

(3 times)

final answer

1.242

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