Algebra: Expressions & Equations

Part 1 – Numerical and Algebraic Expressions

Vocabulary

numerical expression - a mathematical phrase that contains only

numbers and operation symbolsHere are some numerical expressions: 60 + 25 42 ÷ 7 42 – 3Numerical expressions are used daily for

recipes, point totals, and family budgets, among other things.

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 numbersSuppose you knew that the Panthers scored 35 points inthe first half of a game, but you didn’t know how manypoints they scored in the second half. You could use avariable to represent the number of points scored in thesecond 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

Numerical expression

Algebraic expression

contains only

numberscontains a variable

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. twenty-four less than a number, k

2. the product of 7 and 20

3. twelve increased by 17

4. thirty-eight divided by a number, m

5. three less than 5

Guided PracticeEvaluate numerical expressions

1) 7 + 5 x 2

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 PracticeEvaluate 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