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.

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 Numerical expression Algebraic expression contains only numbers contains a variable Numerical expression 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. 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 47 + 65 – 29 32 – 2 (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. x – 7, for x = 15 y3 -12, for y = 3 42 + k – 8, for k = 18 j ÷ 2, for j = 28