1-1: Writing Expressions and Equations

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1-1 Writing Expressions and Equations
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Lesson Opener

• ? represents a number.
• That number plus ten equal 14.
• How do we represent the number algebraically?

?
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WHAT YOULL LEARN

• Translate words into algebraic expressions and
  equations.

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BUILD YOUR VOCABULARY (pages 23)

• An algebraic expression contains numbers and
  variables along with , -, x, and/or .
• A variable is a symbol used to represent an
  unknown number.
• A numerical expression contains numbers along
  with , -, x, and/or .

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BUILD YOUR VOCABULARY (pages 23)

• A factor is a quantity that is being multiplied.
• A product is the result of numbers that are
  multiplied.
• An equation is a mathematical sentence that
  contains an equals sign ().

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• ORGANIZE IT
• In your notes, write
• several words or
• phrases for each of
• the operations,
• addition, subtraction,
• multiplication, and
• division.

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Subtraction
Addition
minus the difference of decreased by less
than fewer than subtracted from
plus the sum of increased by more than added
to The total of
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Division
Multiplication
Divided by The quotient of The ratio of per
Times The product of Multiplied by At Of
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EXAMPLES

• Write an algebraic expression for each verbal
  expression.

p 12
k ? q or kq
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Your Turn

• Write an algebraic
  expression for each verbal expressions
• a) b decreased by 6
• b) the product of 9 and z

b 6
9 ? z or 9z
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A python eats 4 pounds of meat each month.
EXAMPLES

The numerical expression is 4 ? 5 or 4(5).
The algebraic expression is 4 ? d or 4d.
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Write a verbal expression for each algebraic
expression.
EXAMPLES
the sum of 37 and s .
37 s

37 increased by s.
5 (b 3)
5 times the difference of b and 3.
5 multiplied by the difference of b and 3.
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Your Turn

• Write a verbal
  expression for each algebraic expression
• a) x 7
• b) 4 (2n)

X divided by 7
the sum of 4 and the product of 2 and n.
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An equation is a mathematical sentence that
contains an equals sign (). Words are used to
indicate the equals sign. An equation may
contain numbers, variables, or algebraic
expressions.
Equality Equality
Equals Is Is equivalent to Is equal to Is the same as Is as much as Is identical to
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Write an expression for each sentence.
EXAMPLES
The quotient of t and 8 equals 20.

t 8 20 or t/8 20
Seven less than three times g is 31.
3g - 7 31
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Your Turn

• Write an expression for
  each sentence.
• a) A number x increased by 12 is the
  same as 27.
• b) The product of 8 and d decreased by
  9 equals 23.

X 12 27
8d 9 23
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Write a sentence for each equation.
EXAMPLES
j 4 21

Four more than j is equal to 21.
3z 12 11
The product of 3 and z decreased by 12
equals 11.
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Your Turn

• Write a sentence for
  each equation.
• a) r - 10 5
• b)

Ten less than r is equal to 5.
The quotient of n and 3 increased by 6 equals 30.