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Variables in Algebra Variables in Algebra Variable – A symbol, usually a letter of the alphabet, such as the letter x, that is used to represent a number. Variable expression– An expression, such as n – 5, that consists of one or more numbers and variables along with one or more arithmetic operations. (Note: NOOOOO equal sign) Numerical Expression– An expression that represents a particular number. Variables in Algebra Evaluate a Variable Expression – write the expression, substitute a number for each variable, and simplify the result. How Do You Describe a Variable Expression? Variable Expression 5x, 5 · x, (5) (x), 5(x) x 5 ,x 5 x 5 x 5 Meaning 5 times x Operation Multiplication x divided by 5 Division x plus 5 Addition x minus 5 Subtraction State the meaning of the variable expression and name the operation 1. 2. 3. 4. 8 x 2w 7 n 6p A A A A Please click to bypass answer slide Answer: State the meaning of the variable expression and name the operation 1. 2. 3. 4. 8 2 7 6 minus x; Subtraction times w; Multiplication divided by n; Division plus p; Addition You must click on the answer to return to the previous slide Click in the middle of the window to view each answer Evaluate a Variable Expression – write the expression, substitute a number for each variable, and simplify the result. Value of a Variable – A number that may be substituted or assigned to a particular variable; such as n = 3; or x = 5. Example 1: Evaluate each expression when n = 4 a. n3 4+3 Substitute 4 for n. Simplify 7 b. n 3 4-3 1 Substitute 4 for n. Simplify Example 2: Evaluate each expression when x = 8 Substitute 8 for x. Simplify a. 5x 5(8) 40 b. x 4 8¸ 4 2 Note: No operation sign between a variable and number– indicates multiplication problem. Substitute 8 for x. Simplify Example 3: Evaluate each expression when x = 4, y = 6, z = 24. a. Recall: No operation sign between variable(s) and a number– indicates multiplication problem. 5xy Substitute 4 for x; 6 for y. simplify 5xy = (5)(4)(6) = (20)(6) 120 b. zy 24 ¸ 6 4 Evaluate each expression when a = 6, b = 12, and c = 3 1. 4ac A 2. 3. a c a bc A 4. ba A 5. bc A 6. c b A A Click in the middle of the window to view each answer Evaluate each expression when a = 6, b = 12, and c = 3 1. 4ac Notice that all the numbers and letters are together and that there are no operation symbols which indicates that this is a multiplication problem. 4ac (4)(6)(3) ( 24)(3) 72 Substitute the value for a = 6 and c = 3 into the problem and multiply multiply Simplified Click to return to “You try it” slide Click in the middle of the window to view each answer Evaluate each expression when a = 6, b = 12, and c = 3 a c 2. Division Problem a c 6 3 Another way to solve division problems is to write them as fractions and simplify. 2 Substitute the value for a = 6 and c = 3 into the problem and divide Simplified a 6 a c 2 c 3 Click to return to “You try it” slide Click in the middle of the window to view each answer Evaluate each expression when a = 6, b = 12, and c = 3 3. a bc Addition problem a b c 6 12 3 18 3 21 Substitute the value for a = 6, b=12, and c = 3 into the problem, then add Add Simplified Click to return to “You try it” slide Click in the middle of the window to view each answer Evaluate each expression when a = 6, b = 12, and c = 3 4. ba multiplication problem ba (12)(6) 72 Substitute the value for b=12 and a = 6 into the problem, then multiply Simplified Click to return to “You try it” slide Click in the middle of the window to view each answer Evaluate each expression when a = 6, b = 12, and c = 3 5. bc Subtraction problem b c 12 3 9 Substitute the value for b=12 and a = 3 into the problem, then Subtract Simplified Click to return to “You try it” slide Click in the middle of the window to view each answer Evaluate each expression when a = 6, b = 12, and c = 3 6. Divide both numerator and denominator by the GCF = (3) to reduce this fraction. c b Division problem c b 312 3 12 3 3 1 12 3 4 Substitute the value for c=3 and b = 12 into the problem, then Divide Note: It is better to rewrite this division problem as a fraction. This fraction can now be reduced to its simplest form. Simplified It is OK to have a fraction as an answer. Click to return to “You try it” slide