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Variables and Expressions Objective • To evaluate expressions having as many as 3 variables. • Why? To master one aspect of Algebra and Functions in 6th grade math (and beyond) of whole numbers and decimals. Evaluating variables and expressions is a key component in Algebra and other higher math. Vocabulary • Variable - A letter used to stand for a number in an expression or equation. 2x; 6 + x; … • Expression - A mathematical phrase made up of a combination of variables and/or numbers and operations. Expression with variables are also called algebraic expressions. Expressions with variables must have a number to substitute the variable and then solve. • 5n, n = 4. 5 x 4 = 20; 4x – 7; (5 x 2) – 6/3; … • Equation – A number sentence stating that two expressions are equal. • 3 + 5 = x; 8x = 32; … How to Evaluate Expressions Using Variables 1) Substitute the named numbers for the named variables. 2) Solve by using Order of Operations. 3) Remember: Parentheses are solved first. Exponents are next. Multiplication and division are next (from left to right). Addition and subtraction are last (from left to right). 4) Show all steps and Check your work. A) 3x + y; x = 5 and y = 6 = 3(5) + 6 = 15 + 6 = 21 B) 2a + (5b – 4c); a = 15, b = 16, c = 0 = 2(15) + (5x16 – 4x0) = 30 + (80 – 0) = 30 + 80 = 110 Try It! Evaluate each expression for a = 10 and b = 5 1) a + b 2) a x b 3) a – b 4) a ÷ b 1) 10 + 5 = 15 2) 10 x 5 = 50 3) 10 – 5 =5 4) 10 ÷ 5 =2 Evaluate each expression for x = 10, y = 7, z = 2 5) 2x + 3y 6) 4x – 5y + 4z 7) 6y ÷ 3z 8) (x + y) – 2z 5) 41 6) 13 7) 7 8) 13