1 3 Algebraic Expressions and Terms Expressions You

1. 3 Algebraic Expressions and Terms

Expressions You are familiar with the following type of numerical expressions: 12 + 6 3 (12) 6 (3 + 2) 15 - 4 (6)

Definitions n n Variable – A variable is a letter or symbol that represents a number (unknown quantity). 8 + n = 12

Definitions A variable can use any letter of the alphabet. nn + 5 nx – 7 n w - 25 n

Algebraic Expressions When variables are used with other numbers, parentheses, or operations, they create an algebraic expression. a + 2 (a) (b) 3 m + 6 n - 6

What are coefficients? A coefficient is the number multiplied by the variable in an algebraic expression. Algebraic Expression 6 m + 5 Coefficient 6 8 r + 7 m + 4 8, 7 14 b - 8 14

What are constants? n A constant is a number that cannot change its value. In the expression: 5 x + 7 y - 2 the constant is - 2.

What is a term? A term is the name given to a number, a variable, or a number and a variable combined by multiplication or division. Algebraic Expressions a + 2 3 m + 6 n - 6 Terms a, 2 3 m, 6 n, - 6

Figure it out! Identify the terms, coefficients, and constants. 1. 2. 3. 4. 12 a - 6 b + 4 4 x - 2 y c - 32 3 x + 2 Terms Coefficients Constants

Evaluate n Evaluate an algebraic expression – To find the value of an algebraic expression by substituting numbers for variables. m+8 nr – 3 n m = 2 2 + 8 = 10 r=5 5– 3=2

Simplify n Simplifying Algebraic Expression – Combine like terms and complete all operations m=2 nm + 8 + m =2 m+8 n (2 x 2) + 8 4 + 8 = 12

Solving Algebraic Expression When solving real-world problems, you will need to translate words, or verbal expressions, into algebraic expressions.

Write Algebraic Expressions for These Word Phrases Ten more than a number n + 10 w-5 n A number decrease by 5 n 6 less than a number x-6 n+8 n A number increased by 8 n The sum of a number & 9 n + 9 y+4 n 4 more than a number n

Key words to look for: n Addition: n Add n Plus n Sum n Total n Increased by n More than n Subtraction: n Minus n Difference n Subtract n Less than n Decreased by n less

Cont… n Multiplication n Product n Times n Multiply n Double n Of n for n Division n Quotient n Divided by n Splite by

Write algebraic expressions for these word phrases 1. Four more than s S+4 2. The product of 7 and c 7 c 3. 4. Nine less than x X-9 A number divided by the sum of 4 and 7. x/(4+7)

Write algebraic expressions for these word phrases 1. Twice the sum of a number plus 4. 2. The sum of ¾ of a number and 7. 3. Ten times a number increased by 150.

Write an algebraic phrase for these situations 1. The plumber double her bill. 2 x b = 2 b 2. Thirty-five fewer people came than the number expected. X-25

Evaluate each algebraic expression when x = 10 x+8 n x + 49 nx + x nx - 7 n 42 - x n 18 59 2 0 3 32

Complete This Table x 5 10 21 32 x+6 11 16 27 38