Praxis 5001 Section 5003 Math Section: Evaluating and Manipulating Algebraic Expressions, Equations, and Formulas

A local school is holding a raffle as a fundraiser. The individual cost of participating in the raffle is given by the following expression: 5t + 3. Where (t) represents the number of tickets someone purchases. Evaluate expression when (t)=1, (t)=8, and (t)=10 * sample of evaluating simple algebraic expressions for given values of variables

(5t + 3) (t)=1 =((5)(1) + 3) =5 + 3 = 8 (t)=8 =((5)(8) + 3) =40 + 3 = 43 (t)=10 =((5)(10) + 3) =50+ 3 = 53

Jack is buying a pony made of diamonds. The price of the pony is (P) dollars, and Jack also has to pay a 25% diamond pony tax. Match the expressions that the fits the problems: 1. The price of the diamond before tax. 2. The amount of tax Jack pays. 3. Jack's total bill for the diamond. Select from list below: A. P B. 0.75P C. 0.25P D. P+0.25P E. 1.25P F. P/1.25 or P divided by 1.25

1. The price of the diamond before tax. A. P 2. The amount of tax Jack pays. C. 0.25P 3. Jack's total bill for the diamond. D. P+0.25P and/or E. 1.25P P+ 0.25P = 1.25P

Rewrite the expression 4 (8+3) using the distributive law of multiplication over addition. Simplify the expression. (*the use of distributive property to generate equivalent linear algebraic expressions)

4 (8 + 3) 4 x 8 + 4 x 3 32 + 12 44

Define term in an algebraic expression?

An expression involving letters and/or numbers (called factors), multiplied together.

Evaluate simple algebraic expressions for given values of variables

Example: 4 (8 + 3) -distributing (4) to (8) and (3): 4 (11)= 44

Adds and subtracts linear algebraic expressions: Problem 1: Simplify 13x + 7y − 2x + 6a Problem 2: Simplify −5[−2(m − 3n) + 4n] Problem 3: Simplify −[7(a − 2b) − 4b]

Problem 1: Simplify 13x + 7y − 2x + 6a 13x + 7y − 2x + 6a So we group together the terms we can subtract, and just leave the rest: (13x − 2x) + 6a + 7y = 6a + 11x + 7y -------------------------------------------------------------------------------- Problem 2: Simplify −5[−2(m − 3n) + 4n] The first thing we do is expand out the round brackets inside. −2(m − 3n) = −2m + 6n The negative times negative in the middle gives positive 6n. [−2m + 6n + 4n] = [−2m + 10n] Remembering the −5 out front, our problem has become: −5[−2m + 10n] = 10m − 50n Taking each term one at a time, what we did was: −5 × −2m = 10m (Two negative numbers multiplied together give a positive); and −5 × 10n = −50n (Negative times positive gives negative) −5[−2(m − 3n) + 4n] = 10m − 50n -------------------------------------------------------------------------------- Problem 3: Simplify −[7(a − 2b) − 4b] −[7(a − 2b) − 4b] = −[7a − 14b − 4b] = −[7a − 18b] = −7a + 18b

Translate between verbal statements and algebraic expressions or equations

Verbal Statement Algebraic Expression -------------------------------------------------------------------------------- 1.Five increased by four times a number 5 + 4n 2.Eight less than twice a number 2n - 8 3.Three times a number, increased by 9 3n + 9 4.The product of 4, and a number decreased by 7 4(n - 7) 5. The number of feet in x yards. 3x 6. Express the width of a rectangle which is seven less than its length, l. l - 7 7.A number repeated as a factor 3 times. n • n • n = n3

Uses formulas to determine unknown quantities Sample Problem: Given that length a=2 and length c=4 find the value of length b.

a^2 + b^2 = c^2 b^2= c^2 - a^2 b= (square root) c^2 - a^2 b= (square root: (4)^2 - (2)^2 b= (square root: 16-4) =(square root: 12)

What is a linear algebraic expression?

an algebraic expression made up only from any or all of these: Constants; Variables; Addition; Multiplication by constants; Taking opposites (optional); Subtraction (optional); Division by nonzero constants (optional).

Differentiates between algebraic expressions and equations.

equation-has a left side and an equal sign (=) separating the sides. Ex: 3x-7=2 expression-does not have any sides and no (=) sign. Ex: 3x-7