Algebraic Expressions Definitions Variable A variable is a
Algebraic Expressions
Definitions • 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. (expect o and needs to be lower case) • n+5 • x– 7 • w - 25
Definitions • Algebraic Expression – an expression that contains at least one variable, operation, and constant • m+8 • r– 3
Definitions • A constant is a number that does not change. • A coefficient is a number multiplied or divided by a variable. 6 x + 5 6 is the coefficient, x is the variable, and 5 is the constant.
Definitions • A term is a part of an expression that are added or subtracted 5 x + 6 – 4 x This expression has 3 terms: 5 x, 6, and 4 x • A like term are terms who have the same variable raised to the same power In the expression above, 5 x and 4 x are like terms
Definitions • Simplify – Combine like terms and complete all operations m=2 • m+8+m 2 m+8 • (2 x 2) + 8 4 + 8 = 12
Notes • In order to translate a word phrase into an algebraic expression, we must first know some key word phrases for the basic operations.
On the back of your notes: Addition Subtraction Multiplication Division
Addition Phrases: • • More than Increase by Greater than Add Total Plus Sum
Backwards Words Add 3 and 7 = 3 + 7 The sum of 3 and 7 = 3 + 7 3 increased by 7 = 3 + 7 The total of 3 and 7 = 3 + 7 3 more than 7 = 7 + 3 3 added to 7 = 7 + 3
Subtraction Phrases: • • Decreased by Difference between Take Away Less Subtract Less than* Subtract from*
Backwards Words 7 subtract 3 = 7 - 3 The difference of 7 and 3 = 7 - 3 7 decreased by 3 = 7 - 3 7 diminished by 3 = 7 - 3 7 less than 3 = 3 - 7 7 subtracted from 3 = 3 - 7
Multiplication Phrases: • • • Product Times Multiply Of Twice or double Triple
Notes • Multiplication expressions should be written in side-by-side form, with the number always in front of the variable. • 3 a 2 t 1. 5 c 0. 4 f
Division Phrases: • • Quotient Divided by Split equally
Notes Division expressions should be written using the fraction bar instead of the traditional division sign. •
Write Algebraic Expressions for These Word Phrases • Ten more than a number • A number decrease by 5 • 6 less than a number • A number increased by 8 • The sum of a number & 9 • 4 more than a number n + 10 w-5 x-6 n+8 n+9 y+4
Write Algebraic Expressions for These Word Phrases • A number s plus 2 • A number decrease by 1 • 31 less than a number • A number b increased by 7 • The sum of a number & 6 • 9 more than a number s+2 k-1 x - 31 b+7 n+6 z+9
Translate the following phrases. 1) Five plus x minus 3 5+x-3 2) Three times y less 4 3) Eight multiplied by y minus 7 8 y - 7 4) The product of 10 and m decreased by 7 10 m - 7 5) Four more than the quotient of x and 3 6) Six times m plus 8 6 m + 8
Write a variable expression to represent the following if x represents your age. 1) Your age 5 years ago. 2) Twice your age. 3) Your age in 8 years.
Match each phrase with its variable expression. d 1) Twice the sum of x and 3 a) 2 x - 3 e 2) Two less than the product of 3 and x b 3) Three times the difference of x and 2 a 4) Twice a number x less 3 c 5) Two more than 3 times a number x b) 3(x-2) c) 3 x + 2 d) 2(x + 3) e) 3 x - 2
Definitions • Evaluate an algebraic expression – substitute numbers for variables and simplify. • m+8 • r– 3 m=2 r=5 2 + 8 = 10 5– 3=2
Evaluate each algebraic expression when x = 10 • x+8 • x + 49 • x+x • x-7 • 42 - x 18 59 20 0 3 32
Complete This Table n 5 10 21 32 n-3 2 7 18 29
Complete This Table x 5 10 21 32 x+6 11 16 27 38
Translate the verbal phrase into a numerical expression and evaluate 1) The difference of 8 and 1. 2) The product of 12 and 6. 3) The sum of 5 and 9. 4) The quotient of 12 and 3.
- Slides: 27