Order of Operations  PEMDAS. Rules for Multiplying or Dividing Positive/Negative Numbers


 Shannon Gardner
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1 Order of Operations  PEMDAS *When evaluating an expression, follow this order to complete the simplification: Parenthesis ( ) EX. (52)+3=6 (5 minus 2 must be done before adding 3 because it is in parenthesis.) Exponents 3 2 EX. 3 2 (4)=36 (3 2 must be done before multiplying by 4 because exponents come before multiplying.) Multiplication x,. EX. 3x25=1 (3 times 2 must be done before subtracting 5 because multiplying comes before subtraction.) Division  EX. 4/21=1 (4 divided by 2 must be done before subtracting 1 because division comes before subtraction.) Addition + EX =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. +, (+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. +, 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)
2 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. 3+4=+7 (A positive plus a positive gives us a larger positive) 72=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. +83=+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)
3 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 (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 final answer 6 2 = = 4 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) multiples of 4: 4, 8, 12, 16 multiples of 5: 5, 10, 15, 20 multiples of 8: 8, 16, 24 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: becomes becomes *Now, just add or subtract the numerators final answer final answer = =
4 MULTIPLYING FRACTIONS * When multiplying fractions, simply multiply numerator times numerator and denominator times denominator. Example x = = * Now see if the fraction in your answer can be reduced final answer 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: * Now, just multiply becomes 4 x 3 1 x x 3 = = * Now see if the fraction in your answer can be reduced final answer 4 final answer 5 15
5 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 MULTIPLYING DECIMALS * When multiplying decimals, first multiply the numbers as if the decimals don t exist. Example x.2 x * Next, count up the amount of numbers that are to the right of any decimal points..3 2 numbers to numbers to x.2 the right of the decimal x.23 to the right of the decimal 6 (3 and 2) 162 (4, 3, and 2) * Place your decimal at the end of the answer x.2 x * Now, move the decimal to the left..3 (2 times) 5.4 (3 times) x.2 x final answer final answer 1.242
6 DIVIDING DECIMALS Example * When dividing numbers with decimals, place your divisor (outside number/# dividing by) and dividend (inside number/# being divided) in the correct places * 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 Once Once Twice * Count how many numbers you had to move the divisor (outside number) to the right Once Once 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) Once Once Twice * Divide regularly * The decimal point in the dividend (inside number goes straight up. Final answer Final answer Final answer 12
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