380331689-Order-of-Operations- Pemdas-2 PDF

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Orden de Pemdas...

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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 5

2 5

6 7

2 7

(6 and 2 are numerators) (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 3 = 5 5

final answer

6 7

final answer

2 4 = 7 7

* 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 4

5 8

5 15

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

1 5

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 4.2

5.1 6 8.1 becomes 8

5 8

5.1 15.1

1.3 5 5.3 becomes 15

*Now, just add or subtract the numerators. 6 8

5 11 final answer = 8 8

5

3

15

15

=

2 final answer 15

3 15

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

2

x

3

3

6 =

4

5

12

•

2

4

20

7

=

14

* Now see if the fraction in your answer can be reduced. 6

•

6

1

6

2

final answer

20

•

12

• •

14

• • • •

2

10

2

7

final answer

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 5

2 3

• •

1 5

• •

3 4

becomes 4 3 x 5 2

1 x 4 5 3

* Now, just multiply. 4 x 3 = 12 5 2 10

1 5

•

4 = 4 3 15

* Now see if the fraction in your answer can be reduced. 12 10

• • • •

2 2

6 5

final answer

4 15

final answer

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 x.2 6

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

5.4 x.23 162 +1080 1242

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

* Place your decimal at the end of the answer. .3 x.2 6.

5.4 x.23 162 +1080 1242.

* Now, move the decimal to the left. .3 (2 times) x.2 .06. final answer .06

5.4 x.23 162 +1080 12. 42.

(3 times)

final answer

1.242

DIVIDING DECIMALS Example

.8 ÷.2 .25 ÷.5 1.44 ÷.12

* When dividing numbers with decimals, place your divisor (outside number/# dividing by) and dividend (inside number/# being divided) in the correct places. .2 .8

.5 .25

.12 1.44

* Next, the decimal in the divisor (outside number) must be moved until it is all the way to the right of all the numbers of the divisor. .2 .8 Once

.5 .25 Once

.12 1.44 Twice

* Count how many numbers you had to move the divisor (outside number) to the right. ..2 .8

..5 .25

Once

Once

.12 1.44 Twice

* Now move the decimal in the dividend (inside number) to the right the same amount of times that you moved the divisor (outside number). 2. .8.

5. .2.5

12. 14. 4.

Once

Once

Twice

* Divide regularly. 4.0 .5 2. 8. 5. 2.5 -8 -25 0 0

12. 12. 144. -12 -24 0 * The decimal point in the dividend (inside number goes straight up. Final answer

Final answer

4 2. 8.

.5 5. 2.5

Final answer

12 12. 144....