Learning how to write and solve algebraic expressions

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Learning how to write and solve algebraic
expressions
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Important Terms
Terms
Definition Example



Variable Using a
letter to represent n, x, or k

a number
Expression A number,
variable, or any 2 n
combination
of numbers,
variables and operation
signs.
Evaluate (Solve) To put in the
value for n 8
variable and
perform the 2 8 10
operation to
find the
answer
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Words that mean adding
words that mean adding example example
the sum of the sum of a number and 5 x 5
more than 5 more than a number x 5
plus a number plus two x 2
added to 6 added to a number x 6
increased by a number increased by 3 x 3
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Words that mean subtracting
words that mean subtracting example example
less than 5 less than a number x - 5
less 5 less a number 5 - x
minus 5 minus a number 5 - x
subtract from subtract 5 from a number x - 5
reduced by a number reduced by 5 x - 5
decreased by a number decreased by 5 x - 5
diminished by 5 diminished by a number 5 - x
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Words that mean multiplying
Words that mean multiplying example example
multiply multiply a number by 3 3x
multiplied by a number multiplied by 3 3x
times 4 times a number 4x
double double a number 2x
twice twice a number 2x
triple triple a number 3x
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Words that mean dividing
Words that mean dividing example  
divided by a number divided by 5 X/5
divide into divide 5 into a number x/5
the quotient of the quotient of a number and 3 x/3
half of half of a number x/2
one third of one third of a number x/3
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When writing an expression

• You will have a number, a variable, and an
  operation sign
• 8 n

Variable
Number
Operation
8
Writing the Expression in Words

• 8 n
• Write out the number, put in a word or phrase
  that means the operation, and write some number
  or a number when writing the variable. DO NOT put
  the letter (n, x, p).
• Eight increased by some number

Variable
Number
operation
Variable
Number
operation
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Than, to, from

• Whenever you see the words Than, To, From in an
  expression that means you have to flip the places
  of the number and variable.
• Subtract 9 from some number
• X 9

Number
Variable
Operation
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Lets write an expression

• Kim has 5 less pumpkins than Fred.
• We can use a variable (a letter like x or p) to
  stand for the number of pumpkins Fred has.

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• We can compare the number of pumpkins Fred has
  with number of pumpkins Kim has by using a
  mathematical expression that uses a variable.
  Mathematical expressions that use variables are
  called algebraic expressions.

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• Lets write this as an algebraic expression.
  Lets use p as a variable to represent the number
  of pumpkins Fred has. 5 less tells us the number
  we should use and the operation.
• p - 5

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• Lets evaluate the expression by putting in a
  value for our variable. Lets say Fred has 15
  pumpkins . That means that we now know that p
  15. Now we can figure out how many pumpkins Kim
  has.
• P15
• P - 5 K
• 15 5 k
• K 10

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• Lets write an algebraic expression in words.
• n 3
• Some number minus three
• or
• some number subtract three

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• Write an algebraic expression for each word
  phrase.
• Some number plus 6
• 8 less than a number

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evaluating expressions

• When evaluating expressions just plug in the
  number for the variable.
• k 13
• k 7
• 7 13
• 7 13 20

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Solving expressions

• Change each algebraic expression into words. Then
  evaluate when n 4
• n 9
• 11 n
• 14 r
• P - 4

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• Will these expressions give us the same answer if
  we substitute the same number for the variable?
• 8 plus a number
• 8 more than some number

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• Will these expressions give us the same answer if
  we substitute the same number for the variable.
• 8 less than a number
• some number minus 8

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Worksheet websites

• http//www.teachervision.fen.com/tv/printables/Mat
  h_5_PS_5-8.pdf
• http//itech.pjc.edu/falzone/worksheets/translate_
  phrases_to_var_expr1.pdf