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Today we are going to: • write algebraic expressions by representing unknown quantities; and • evaluate algebraic expressions by substituting the given value for the variable. Write an algebraic expression for each of the following statements. (a) Add 3 to p p+3 (b) Subtract 2 from the product of 3 and x 3x – 2 (c) Divide the sum of m+n m and n by 5 5 (d) Multiply 7 to half of t 7t 2 Algebraic Expression in Two or more unknown Example : State the number of unknown in each of the following algebraic expressions. (a) 2a + 2b (b) 100 – 2pqr (c) hjk + 8p – 19q Answer : • 2a + 2b has two unknown : a and b • 100 – 2pqr has three unknown : p, q and r • hjk + 8p – 19q has five unknown : h, j, k, p and q Evaluating Algebraic Expression *To evaluate an algebraic expression is to find the value of the expression. STEPS: 1. Substitute the given value for the variables (replace letters with the given numbers) 2. Solve using the order of operations (PEMDAS) Example : Evaluate 2x + 5y when x = 4 and y=2 Solution : 2x + 5y = 2 (4) + 5 (2) = 8 + 10 = 18 Evaluate p+2q+ 3r given p = 2 q = 4, r = 6 =2+ 2(4) + 3(6) =2 + 8 + 18 =28 Example : Evaluate 3c + 5 if c = 5 and d = 1 4d Solution : 3c + 5 = 3 (5) + 5 4d 4 (1) = 15 + 5 4 = 20 4 = 5 ALGEBRAIC EXPRESSIONS Step 1 Substitute the given values for the variables. Step 2 Solve using the order of Operations PEMDAS. Problem 1 Given the formula P=2L+2W, find the value of P if K=7 and W=3. Problem 2 If V=lwh, what is the value of V when l=2, w=3, and h=4? Problem 3 If x=1 and y= -2, which expression has a value of 3? (a) x+y (c) x-y (b) xy (d) y-x Problem 4 If a=1 and b=-2, find the value of 2 (a+b) . Problem 5 Using the formula 2 V=x h, find V when x=6 and h=2 Problem 6 Evaluate the 2 expression (6a) b if a=2 and b=-1 Problem 7 Find the value of 3a-4b if a=-2 and b=5. Problem 8 Find the value of 2 (x -8x+4) if x=1/2. Problem 9 2 5a -b Evaluate if a=-2 and b=10. Problem 10 Find the value of 3 the expression 3x when x=-2 Problem 11 What is the value of R=5 and S=-2. 2 RS if Problem 12 Evaluate the expression 2 3x +y if x=1 and y=-3. Problem 13 Find the value of the 3 expression 2xy if x=3 and y=-2 Problem 14 Find the value of x=-3. 2 5x if Problem 15 If x=-3 and y=2, find the 2 value of (xy) .