Transcript Variable and Expressions

Variable and Expressions
Variables and Expressions
 Aim:
– To translate between words and algebraic
expressions.
-- To evaluate algebraic expressions.
Vocabulary
 A variable is a letter used to represent an unknown
quantity.
Ex. x y z k m a
 A constant is a value that does not change.
Ex. 5 –7 13.18 π
 A numerical expression may contain only constants,
operations, and grouping symbols.
Ex. 4 – 52 + 8 ÷ 2
Vocabulary
 An algebraic expression (or variable expression)
may contain anything in a numerical expression, but it also
contains one or more variables.
Ex. 3x² – 4x + 3
 An equation states that two expressions are equal.
Ex. 5x – 3 = 7x + 5
 A term is a constant, variable, or product or quotient of a
variable and a constant.
Ex. 3 x 4y w/3
Vocabulary
 To evaluate an expression, condense it into a single value
using the order of operations.
 – Algebraic expressions can only be
evaluated if we know the value of all
variables.
 To simplify an algebraic expression, combine all like terms
and follow any applicable algebraic and exponent laws.
 To solve an equation, isolate the given variable on one side
and simplify the other side.
Example
 Evaluate each expression.
(3 + 9) ÷ 3
12 ÷ 3
Simplify the contents of the parentheses.
4
Divide.
9 + 12 ÷ 3
9+4
13
Divide.
Add.
Example
 Evaluate each expression when a = 2 and b = –3.
4a + 5b
4(2) + 5(–3)
8 + (–15)
–7
–2a – b – b²
–2(2) – (–3) – (–3)²
–2(2) – (–3) – 9
–4 – (–3) – 9
–10
Plug in the given values.
Multiply.
Add.
Plug in the given values.
Evaluate the power.
Multiply.
Subtract from left to right.
Translating into Algebra
 A large part of this course involves writing your own
algebraic expressions or equations from word problems.
 The following information provides some hints for knowing
which operation is implied in word problems.
– Note: This information is not all-inclusive.
Nor is it a guarantee of which operation to use (consider “per”
and “each”). It simply lists common phrases for each
operation.
Addition
 The sum is the answer to an addition problem.
 Key words / phrases: sum, increased
by, put together, combine, more
 Example: x + 3
The sum of x and 3.
Three more than x.
x increased by 3.
Subtraction
 The difference is the answer to a subtraction problem.
 Key words / phrases: difference, less than, how much more, how
much less, reduced by, fewer, decreased by
 Example: x – 7
The difference of x and 7.
Seven less than x.
x decreased by 7.
Multiplication
 The product is the answer to a multiplication problem.
 Key words / phrases: product, times,
equal groups, put together, per, each
 Example: 4x
The product of 4 and x.
Four times x.
Four equal groups of x.
Division
 The quotient is the answer to a division problem.
 Key words / phrases: quotient, divided by, split into equal groups,
separated, per, each
 Example: x ÷ 6
The quotient of x and 6.
x divided by 6.
Six divided into x.
Example
 Jonathan reads 20 pages per hour.
 Write an algebraic model for the number
of pages he reads in h hours.
20h
 Renequa is 3 years younger than José,
who is j years old. Write an algebraic model for Renequa’s age.
j–3
Example
 You have $10.
Write an algebraic model for the amount you have left if you
buy b bottles of water that cost $0.85 each.
$10 – $0.85b
 Paul can run one mile in 6 minutes.
Write an expression for the number of miles that Paul can run
in m minutes.
m÷6