Assessments

Unit 8 Test

Wednesday, March 14

Order of Operations

Points to Remember

  • PEMDAS- parentheses, exponents, multiplication and/or division, addition and/or subtraction.
  • REMEMBER: JUST BECAUSE WE SAY MULTIPLICATION AND DIVISION AND ADDITION AND SUBTRACTION DOES NOT MEAN YOU DO MULTIPLICATION BEFORE DIVISION OR ADDITION BEFORE SUBTRACTION. DO WHICHEVER EVER OPERATION THAT COMES FIRST WHEN READING THE PROBLEM FROM LEFT TO RIGHT.
  • When solving a problem with parentheses inside another set of parentheses or any other grouping, start working with the innermost set of parentheses' and continue until everything in the groupings have been solved.
  • If an expression has a line of division and numbers on either side of the fraction, solve what's on top first, then what's below the line , divide the top by the bottom and then complete the rest of the expression.
  • If an exponent is above a number inside parentheses, solve the exponent first before doing any other operations. If the exponent is outside of the parentheses, complete the operations inside the parentheses until there is only one number left, then the exponent applies to that number and can be solved.

Properties of Addition and Multiplication

Points to Remember

  • Associative Property will have the same numbers usually (but not always) in the same order but the parentheses will be around different numbers. Even if the numbers have moved focus on the parentheses because the Associative Property states that no matter which numbers are added or multiplied first, the answer will still be the same.
  • Commutatitve Property will have the numbers in different places. Remember commuters travel so the numbers will move or travel to a different position with the commutative property but the answer will be the same.
  • Identity Properties state that when adding a number and 0, the answer will be the non zero number- the number keeps its identity. When multiplying a number by 1, the answer will be the number itself-it keeps its identity.
  • Inverse Properties add or multiply opposites or reciprocals. The Additive Inverse property will have an integer being added with its opposite ( 3 + -3=0). A problem displaying the additive inverse property will always have a an answer of 0. The Multiplicative Inverse Property multiplies a fraction by a whole number or a fraction. As we have learned, when multiplying whole numbers by fractions, the whole number is placed over 1 so that it is in fraction form but keeps its same value. SO if a fraction is being multiplied by a whole number, remember that the whole number should be placed over which will make it the inverse (reciprocal, opposite) of the other fraction.
  • WITH THE INVERSE AND IDENTITY PROPERTIES REMEMBER THAT ADDITION WILL DEAL WITH 0. WITH THE INVERSE THE ANSWER WILL BE 0 AND WITH THE IDENTITY 0 WILL BE ADDED TO A NUMBER. MULTIPLICATION WILL DEAL WITH 1. WITH THE INVERSE THE ANSWER WILL BE 1. WITH THE IDENTITY THE A NUMBER WILL BE MULTIPLIED BY 1.
  • The Zero Property of Multiplication states that any number multiplied by 0 will have an answer of 0.
  • Multiplication can be shown with x, a dot, or a number beside a parentheses.