Variables and Expressions

1
Variables and Expressions

• Lesson 1-10

2
What is a variable?

• A quantity that can change or vary
• Quantity means you can count it
• It is represented by a letter

We often confuse the words quality and
quantity. Quality means How good is it?
(good, bad, fair, etc.) Quantity means How much
do you have? (a number)
3
What does substitute mean?

• When a substitute fills in for a teacher, the
  sub takes the teachers place.
• When you substitute numbers for a variable, you
  put a number in a variables place.

4
Words that you NEED to know

• Evaluate
• Solve
• Sum - (suma)
• The answer to an addition problem
• The total
• Difference (diferencia)
• The answer to a subtraction problem
• Product (producto)
• The answer to a multiplication problem
• Quotient (cociente)
• The answer to a division problem

5
Expression versus Equation

• Expression
• No equal sign
• a b
• p q
• Equation
• Has an equal sign
• a b 12
• p q 15

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We use substitution to solve expressions

• Expressions like ab cannot be solved without
  substituting numbers for the variables
• If there are no numbers, then there are no
  solutions.
• ab will always be ab
• Always look to see if the variables have been
  assigned a number
• If variables are supposed to change to numbers,
  then there is a solution
• Solve the expression, a b, if a4 and b2
• if a4 and b2, then ab is 42
• 426

7
The different ways we show multiplication and
division in algebra

• Division
• a b
• a/b

• Multiplication
• We usually do not use x for multiplication in
  algebra because x is a variable.
• a b
• a b
• a(b)
• ab

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Another thing to note

• When you see 2 variables (or a number and a
  variable) back to back, they are really inside of
  invisible parentheses!
• ab (a b)
• 5a (5 a)

9
Sample problems
10
Before we get started

• Many times, if a problem does not make sense to
  you, the answer is in the directions!
• ALWAYS read the directions
• You will need the order of operations to solve
  these correctly!

11
Evaluate each expression if a10 and b5
10 5
10 5
15
50
10 - 5
10 5
5
2
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What does it mean if there is a letter and a
number together, but there is no sign?
- x

• Multiply them together.
• They cannot be separated
• Think of them as a leg and a foot or an arm and a
  hand.
• You CANNOT rip them apart.
• They must stay together unless you surgically
  take them apart with an operation (, -, x, )

13
Evaluate this expression if x 10, y 7, and z
2
When you have a number and a variable together,
you have to keep them together. This is why we
use parentheses.
We dont have a variable z, so we do not use this
one.
2x 3y
(2 10) (3 7)
(20) (21)
41
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Evaluate this expression if x 10, y 7, and z
2
4x - 5y 4z
(4 10) (5 7) (4 2)
40 - 35 8
5 8
13
15
Lets Practice
16
Evaluate this expression for x 9, y 1, and z
25

• x y z

Remember Multiplication always comes before
addition!
9 1 25
9 25
34
5
17
Evaluate this expression for x 9, y 1, and z
25

• 2(xy)

Remember Always do the parentheses first!
2(91)
Remember If you see a number against the
parentheses, it means you have to multiply.
2(10)
20
4
18
Evaluate this expression for x 9, y 1, and z
25

• 2z 5y

(2 25) (5 1)
50 5
10
3
19
Evaluate this expression for x 9, y 1, and z
25

• 4x (25y z)

(4 9) (25 1) 25
(36) (25) 25
(36) 0
0
2
20
Evaluate this expression for x 9, y 1, and z
25

• 2 (x y)

2 (9 1)
2 (8)
16
1