Pre-Algebra Review  Chapter 1, Sections 1 and 2 By Ms. Dewey-Hoffman, 2009  http://msdhpowerpoints.blogspot.com/
Section 1: Variables and Expressions <ul><li>Variables </li></ul><ul><ul><li>Are letters or symbols that act as placeholde...
Language of Math: Operations <ul><li>Addition:  Total ,  Sum ,  Altogether ,  Increase , and  Combine . </li></ul><ul><li>...
Operations and their Parts: Multiplication & Division <ul><li>Two numbers in a multiplication problem are called the  FACT...
Writing Variable Expressions: Example Problems <ul><li>Nine more than number y     y + 9 </li></ul><ul><li>A number z tim...
Section 2: The Order of Operations <ul><li>Simplify an Expression </li></ul><ul><ul><li>To replace the expression with the...
The Order of Operations: PEMDAS <ul><li>P  :  Do operations inside  PARENTHESES  (or other delimiters/grouping symbols, li...
Example Problems: Show each Step of PEMDAS <ul><li>2[(13 – 4) ÷ 3] = </li></ul><ul><li>1 +  10 – 2  = </li></ul><ul><li>  ...
Assignment #1 <ul><li>Pages 6-7: 10-44 even. (Show answers only) </li></ul><ul><li>Page 11: 10-30 even. (Copy problem and ...
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Chapter 1, Section 1&2

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Chapter 1, Sections 1 and 2, Expressions and Order of Operations.

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Chapter 1, Section 1&2

  1. 1. Pre-Algebra Review Chapter 1, Sections 1 and 2 By Ms. Dewey-Hoffman, 2009 http://msdhpowerpoints.blogspot.com/
  2. 2. Section 1: Variables and Expressions <ul><li>Variables </li></ul><ul><ul><li>Are letters or symbols that act as placeholders for numbers. </li></ul></ul><ul><ul><li>One letter = One number. </li></ul></ul><ul><li>Simplify </li></ul><ul><ul><li>To replace a variable with a number. </li></ul></ul><ul><li>Expressions: Numerical and Variable </li></ul><ul><ul><li>Expressions don’t have an equal sign. 50 + 10  Expression </li></ul></ul><ul><ul><li>Equations do have an equal sign. 50 + 10 = 60  Equation </li></ul></ul><ul><li>Numerical Expressions </li></ul><ul><ul><li>Only have numbers: 50 + 10  No Variables </li></ul></ul><ul><li>Variable Expressions </li></ul><ul><ul><li>Have at least 1 Variable: 75 + g + 25  At least 1 Variable </li></ul></ul><ul><ul><li>3x + y  At least 1 Variable </li></ul></ul>
  3. 3. Language of Math: Operations <ul><li>Addition: Total , Sum , Altogether , Increase , and Combine . </li></ul><ul><li>Subtraction: Difference , Less Than , More Than , and Decrease . </li></ul><ul><li>Multiplication: Product , Times , and Each . </li></ul><ul><li>Division: Quotient , Share , and Each . </li></ul>Operations and their Parts: Addition & Subtraction <ul><li>Two numbers being added are called ADDENDS. </li></ul><ul><li>The answer to an addition problem is called the SUM. </li></ul><ul><li>The number being subtracted is the SUBTRAHEND and the number from which we are subtracting is called the MINUEND. </li></ul><ul><li>(First Number  Minuend) – (Second Number  Subtrahend) = Difference. </li></ul><ul><li>The answer to a subtraction problem is called the DIFFERNCE. </li></ul>
  4. 4. Operations and their Parts: Multiplication & Division <ul><li>Two numbers in a multiplication problem are called the FACTORS . </li></ul><ul><li>The answer to a multiplication problem is the PRODUCT . </li></ul><ul><li>The number being divided is called the DIVIDEND . The number we are dividing by is called the DIVISOR . </li></ul><ul><li>The answer to a division problem is the QUOTIENT . </li></ul><ul><li>(Top Number  Dividend ) / ( Divisor  Bottom Number) = Quotient </li></ul>
  5. 5. Writing Variable Expressions: Example Problems <ul><li>Nine more than number y  y + 9 </li></ul><ul><li>A number z times three  z x 3 , z • 3 , z3 </li></ul><ul><li>5 times the quantity 4 plus a number c  5 • (4 + c) , 5(4 + c) </li></ul><ul><li>Try These: </li></ul><ul><li>The product of x and y, plus 5  </li></ul><ul><li>The sum of t and u, divided by 4  </li></ul><ul><li>R divided by 5, minus 3, equals 2.  </li></ul><ul><li>Y fewer than 27  </li></ul><ul><li>Daniel has 14 more than Sam.  </li></ul><ul><li>The total of Tommy’s marbles and 13  </li></ul><ul><li>55 subtracted from 105, divided by 5 equals 10.  </li></ul>Challenge problems are in purple.
  6. 6. Section 2: The Order of Operations <ul><li>Simplify an Expression </li></ul><ul><ul><li>To replace the expression with the simplest name for its value… </li></ul></ul><ul><ul><li>or solve as far as possible! </li></ul></ul><ul><ul><li>What does 36 + 25 ÷ 5 simplify to? </li></ul></ul><ul><li>The Order of Operations </li></ul><ul><ul><li>36 + 25 ÷ 5 </li></ul></ul>Division first! 25 ÷ 5 = 5 Rewrite. 36 + 5 Addition second! 36 + 5 = 41 41 is the simplified expression for 36 + 25 ÷ 5
  7. 7. The Order of Operations: PEMDAS <ul><li>P : Do operations inside PARENTHESES (or other delimiters/grouping symbols, like [BRACKETS] and division bars). </li></ul><ul><ul><li>Work from the inside of the Parentheses/Brackets to the outside. </li></ul></ul><ul><ul><li>Division Bars: Simplify the top and bottom first, then divide! </li></ul></ul><ul><li>E : Evaluate terms with EXPONENTS . </li></ul><ul><ul><li>The exponent ONLY effects the NUMBERS/VARIABLES/PARENTHESES in front of the little number (to the left). Example: 5 10 , x 2 , (5 + 8) 3 . </li></ul></ul><ul><li>D M : Do MULTIPLICATION and DIVISION . </li></ul><ul><ul><li>In order from LEFT to RIGHT . </li></ul></ul><ul><ul><li>5 • 10 ÷ 2  5 • 10 = 50, 50 ÷ 2 = 25, 5•10÷2=25 </li></ul></ul><ul><li>A S : ADD and SUBTRACT terms . </li></ul><ul><ul><li>In order from LEFT to RIGHT . </li></ul></ul><ul><ul><li>8 + 7 – 5  8 + 7 = 15, 15 – 5 = 10, 8+7-5=10 </li></ul></ul>PEDMAS is where order REALLY matters!
  8. 8. Example Problems: Show each Step of PEMDAS <ul><li>2[(13 – 4) ÷ 3] = </li></ul><ul><li>1 + 10 – 2 = </li></ul><ul><li> 4 </li></ul><ul><li>4 – 1 • 2 + 6 ÷ 3 = </li></ul><ul><li>5 + 6 • 4 ÷ 3 – 1 = </li></ul>6 3 4 12 <ul><li>Example of Showing Steps: PEMDAS </li></ul><ul><li>2[(13 – 4) ÷ 3] = Copy Problem </li></ul><ul><li>2[(9) ÷ 3] = Simplify Parentheses </li></ul><ul><li>2[3] = Simplify Brackets </li></ul><ul><li>2[3] = 6, Multiply </li></ul><ul><li>6, Answer, Always Boxed! </li></ul>
  9. 9. Assignment #1 <ul><li>Pages 6-7: 10-44 even. (Show answers only) </li></ul><ul><li>Page 11: 10-30 even. (Copy problem and show each step of PEMDAS) </li></ul><ul><li>Extra Credit: Page 11: 36-39 all. (Show problem and answer) </li></ul><ul><li>Start your homework! </li></ul><ul><li>Fold a lined piece of paper in half. (Holes on the Left Side!) </li></ul><ul><li>Top right: Name, Class, Assignment Number, Assignment. </li></ul><ul><li>Start on the left side of the fold and show all work. </li></ul><ul><li>Remember to box your answers! </li></ul><ul><li>Print out of pages 3, 4, 5, and 7 should be pasted in with your notes! </li></ul>

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