1. Algebra: Expressions & Equations
Part 1 – Numerical and Algebraic Expressions

2. Vocabulary numerical expression -
a mathematical phrase that contains only numbers and operation symbols
Here are some numerical expressions:
÷ – 3
Numerical expressions are used daily for recipes, point totals, and family budgets, among other things.

3. Vocabulary
“Evaluating” an expression means to perform the operation(s) in the expression so the final result is a standard number….
the “answer”!

4. 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.

5. Vocabulary algebraic expression
An expression that contains a variable.
Here are some algebraic expressions:
5 + n 7a (means 7 x a) k - 3

6. Vocabulary Numerical expression Algebraic expression
contains only numbers
contains a variable
Numerical expression
Algebraic expression

7. Vocabulary
Identify each as a numerical expression or
an algebraic expression. Explain your answer.
3 + 6
9 – d
x – 12

8. 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

9. Translate Word Expressions
The ability to translate words into symbols is fundamental to solving many word problems and all future work in algebra.

10. 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

11. Translate Word Expressions
Example:
Write a numerical expression for
“nine increased by seven squared”

12. Translate Word Expressions
Example:
Write a algebraic expression for
“nine increased by a number, n” n

13. Translate Word Expressions
Write a numerical expression or algebraic expression for
the word expressions.
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

14. Guided Practice Evaluate numerical expressions
– 29
32 – 2
( ) ÷ 9

15. 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 replace the x with the given value, 12
perform the operation (add) 19

16. Guided Practice Evaluate each algebraic expression for the given value of the variable.
x – 7, for x = 15
y3 -12, for y = 3
42 + k – 8, for k = 18
j ÷ 2, for j = 28