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1-5 Evaluating Algebraic Expressions Preview Warm Up California Standards Lesson Presentation Holt CA Course 1 1-5 Evaluating Algebraic Expressions Warm Up Evaluate. 1. 5(7) – 1 34 2. 7(18 – 11) 49 3. 22 + 17 8 + 3 161 4. 36 + 15(40 – 35) 111 5. 33 + 7(12 – 4) 83 Holt CA Course 1 1-5 Evaluating Algebraic Expressions California Standards AF1.2 Write and evaluate an algebraic expression for a given situation, using up to three variables. Also covered: AF1.3 Holt CA Course 1 1-5 Evaluating Algebraic Expressions Vocabulary variable constant algebraic expression evaluate Holt CA Course 1 1-5 Evaluating Algebraic Expressions The letter a has a value that can change, or vary. When a letter represents a number that can vary, it is called a variable. The year 1954 is a constant because the number cannot change. An algebraic expression is an expression that contains at least one variable. For example, 1954 + a is an algebraic expression. Holt CA Course 1 1-5 Evaluating Algebraic Expressions Age Year born + age = year at age 16 18 21 1954 + 16 1954 + 18 1954 + 21 1970 1972 1975 36 1954 + 36 1990 a 1954 + a To evaluate an algebraic expression, substitute a number for the variable. Holt CA Course 1 1-5 Evaluating Algebraic Expressions Multiplication and division of variables can be written in several ways, as shown in the table. When evaluating expressions, use the order of operations. Holt CA Course 1 1-5 Evaluating Algebraic Expressions Additional Example 1A: Evaluating Algebraic Expressions The expression b + 9 represents Chad’s age when his brother is b years old. Evaluate the expression for each value of b, and then tell what the value of the expression means. b=5 b+9 5+9 14 Substitute 5 for b. Add. When his brother is 5, Chad is 14. Holt CA Course 1 1-5 Evaluating Algebraic Expressions Additional Example 1B: Evaluating Algebraic Expressions The expression b + 9 represents Chad’s age when his brother is b years old. Evaluate the expression for each value of b, and then tell what the value of the expression means. b=2 b+9 2+9 11 Substitute 2 for b. Add. When his brother is 2, Chad is 11. Holt CA Course 1 1-5 Evaluating Algebraic Expressions Additional Example 2: Evaluating Algebraic Expressions Involving Order of Operations Evaluate the expression for the given value of the variable. A. 4x – 3 for x = 2 4(2) – 3 Holt CA Course 1 Substitute 2 for x. 8–3 Multiply. 5 Subtract. 1-5 Evaluating Algebraic Expressions Additional Example 2: Evaluating Algebraic Expressions Involving Order of Operations B. s ÷ 5 + s, for s = 15 15 ÷ 5 + 15 3 + 15 18 Holt CA Course 1 Substitute 15 for s. Divide. Add. 1-5 Evaluating Algebraic Expressions Additional Example 3: Evaluating Algebraic Expressions with More than One Variable Evaluate 6 a + 4b − c, for a = 3, b = 2, and c = 7. 6 + 4b − c a 6 + 4(2) − 7 Substitute 3 for a, 2 for b, 3 and 7 for c. 2+8−7 3 Holt CA Course 1 Divide and multiply from left to right. Add and subtract from left to right. 1-5 Evaluating Algebraic Expressions Check It Out! Example 1B The expression y + 7 represents Sidney’s age when her brother is y years old. Evaluate the expression for each value of y, and then tell what the value of the expression means. y=8 y+7 8+7 15 Substitute 8 for y. Add. When her brother is 8, Sidney is 15. Holt CA Course 1 1-5 Evaluating Algebraic Expressions Check It Out! Example 2 A. 4y2 + 2y, for y = 3 4(3)2 + 2(3) 4(9) + 2(3) 36 + 6 42 Holt CA Course 1 Substitute 3 for y. Evaluate the power. Multiply. Add. 1-5 Evaluating Algebraic Expressions Check It Out! Example 3 Evaluate 8 − x + 2z, for w = 2, x = 3, and z = 4 w 8 − x + 2z w 8 − 3 + 2(4) 2 Substitute 2 for w, 3 for x, and 4 for z. 4−3+8 Divide and multiply from left to right. 9 Holt CA Course 1 Add and subtract from left to right. 1-5 Evaluating Algebraic Expressions Lesson Quiz Evaluate n + 7 for each value of n. 1. n = 25 32 2. n = 31 38 Evaluate each algebraic expression for the given value of the variables. 3. 6y – 5 for y = 7 37 4. 4x2 + 3x for x = 6 162 5. 56 + 3y for x = 4 and y = 3 23 x 6. The expression 7d gives the number of days in d weeks. Evaluate 7d for d = 12. How many 84 days are in 12 weeks? Holt CA Course 1