Algebra:
Expressions & Equations
Part 1 – Numerical and
Algebraic Expressions
Vocabulary
numerical expression a mathematical phrase that contains only
numbers and operation symbols
Here are some numerical expressions:
60 + 25
42 ÷ 7
42 – 3
Numerical expressions are used daily for
recipes, point totals, and family budgets,
among other things.
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Vocabulary

“Evaluating” an expression means to perform
the operation(s) in the expression so the final
result is a standard number….
the “answer”!
Vocabulary

variable
a letter or symbol used to stand for one or
more numbers
Suppose you knew that the Panthers scored 35 points in
the first half of a game, but you didn’t know how many
points they scored in the second half. You could use a
variable to represent the number of points scored in the
second half.
35 + p  total points scored
Use p to represent the points in the second half.
Vocabulary
algebraic expression
An expression that contains a variable.

Here are some algebraic expressions:
5+n
7a (means 7 x a)
k-3
Vocabulary
contains
only
numbers
Numerical expression
contains a
variable
Algebraic expression
Vocabulary
Identify each as a numerical expression or
an algebraic expression. Explain your answer.




3+6
9–d
x – 12
17 + 53
Evaluating numerical expressions


To evaluate a numerical expression, perform
the operations, remembering to follow the
order of operations.
Example: Evaluate 52 x (5-2)
52 x (5-2)
parentheses
52 x 3
exponents
25 x 3
multiply
75
Translate Word Expressions
The ability to translate words into symbols is
fundamental to solving many word
problems and all future work in algebra.
Translate Word Expressions

Writing numerical expressions and algebraic
expressions requires translating words into numbers
and symbols. You can do this by looking for key
words.
Addition
Subtraction
Multiplication
Division
Sum
Difference
Product
Quotient
Increased by
decrease
Factors
Equally divided
More than
Less than
Times
Divided by
plus
minus
Multiplied by
Translate Word Expressions
Example:
Write a numerical expression for
“nine increased by seven squared”
9
+
72
Translate Word Expressions

Example:
Write a algebraic expression for
“nine increased by a number, n”
9
+
n
Translate Word Expressions
Write a numerical expression or algebraic expression for
the word expressions.
1.
2.
3.
4.
5.
twenty-four less than a number, k
the product of 7 and 20
twelve increased by 17
thirty-eight divided by a number, m
three less than 5
Guided Practice
Evaluate numerical expressions
1)
7+5x2
2)
47 + 65 – 29
3)
32 – 2
4)
(35 + 10) ÷ 9
Evaluating algebraic expressions
To evaluate an algebraic expression, replace
the variable with a number and perform the
operation(s) in the expression.
Example: Evaluate x + 7, for x = 12
x+7
replace the x with the given value, 12
12 + 7
perform the operation (add)
19

Guided Practice
Evaluate each algebraic expression for the
given value of the variable.
1)
x – 7, for x = 15
2)
y3 -12, for y = 3
3)
42 + k – 8, for k = 18
4)
j ÷ 2, for j = 28