MAT 150 Unit 3

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MAT 150 Unit 3

• Ch 7 - 1

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Section 7 1 Variable Notation

• Rational Numbers
• Any number that can be expressed as a ratio, or
  quotient, of any integer and non-zero integer.
• Operations with rational numbers follow the same
  rules as integers, including the order of
  operations

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Section 7 1Variable Notation

• Symbolic Representation
• Equation a statement stating two expressions or
  quantities to be equal in value
• Variable a letter or symbol used to represent
  an unknown quantity
• Factors numbers or variables that are
  multiplied
• Terms single quantities or products or
  quotients of quantities

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Section 7 1 Variable Notation

• Coefficient the number in front of a variable
• Like terms terms that are alike, eg. Have the
  same variable and exponent
• Distributive property of multiplication over
  addition
• Symmetric property of equality
• x 5 and 5 x

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Section 7 1 Variable Notation

• Writing symbolic statements from words
• What number added to 5 gives 8?
• What number (x) added to (), gives() 8?
• x 5 8
• A number divided by 5 is 3.
• x/5 3
• Two times a number and 3 is 15.
• 2x 3 15
• The sum of a number and 3 doubled is 14.
• 2(x 3) 14

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Section 7 1 Variable Notation

• Key words
• sum of, plus, increased by, more than
• less than, subtracted from, difference
• is, gives, yields
• x a number, some number, how many
• Examples
• How many shelves that are 3 feet long can be made
  from a board that is 12 feet long?
• x number of shelves
• 3x 12

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Section 7 1 Variable Notation

• Combining LIKE TERMS
• Like terms are terms with the same variable and
  same power. 3x 2x or 6x2 2x2
• When adding, simply add the coefficients and keep
  the variable name the same
• When subtracting follow the subtraction rules and
  change the minus sign to and the number
  following to its opposite

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Section 7 1 Variable Notation

• Examples
• 2x 3x (2 3)x 5x
• 5y 2y 5y ( 2y) 5 ( 2)y 3y
• 3xy 2xy 3xy (2 xy) 3 (2)xy
  5xy
• 4x 3y 4x 3y (unlike terms, cannot be
  added)

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Section 7 1 Variable Notation

• Distributive Property of Multiplication over
  Addition
• 3(x 2) means 3 times the sum of x
  and 2
• since you cannot add x and 2 you
• must distribute the 3
• 3(x) 3(2) multiply 3 times
  everything in
  
  the parenthesis
• 3x 6

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Section 7 1 Variable Notation

• Distributive property
• 5(2x 1)
• 5(2x -1)
• 5(2x) 5(-1)
• 10x (-5) or 10x 5

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Section 7 1 Variable Notation

• 4( 6x ½)
• 4( 6x ½)
• 4( 6x) 4( ½ )
• 24x 2 or 24x 2