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1-1 Variables and Expressions • algebraic expression • product • variable • power • term • exponent • factor • base Vocabulary 1 • Algebraic Expression: Does not have an equal sign and consists of numbers and variables. (ex. 3x+2) • Variable: a letter used to represent an number (ex. a, b, c, x, y,…) • Term: a part of piece of an expression (ex. 3x+2) 3x is called the variable term 2 is called the constant term • Product: the result or solution of multiplying two or more numbers together • Factor: two or more numbers that are multiplied together Ex. 2 × 4 = 8 2 and 4 are factors of 8 8 is the product of 2 and 4 2 • Power: an expression like 𝑥 5 𝑥 5 𝑚𝑒𝑎𝑛𝑠 𝑥 𝑡𝑜 𝑡ℎ𝑒 𝑓𝑖𝑓𝑡ℎ 𝑝𝑜𝑤𝑒𝑟 • It contains an exponent and a base In the example 𝑥 5, 𝑥 is the base of the expression 5 is the exponent 5 𝑥 𝑟𝑒𝑎𝑙𝑙𝑦 𝑚𝑒𝑎𝑛𝑠 𝑥 ∗ 𝑥 ∗ 𝑥 ∗ 𝑥 ∗ 𝑥 Write Verbal Expressions A. Write a verbal expression for 8x2. Example 1 3 Write Verbal Expressions B. Write a verbal expression for y5 – 16y. Example 1 A. Write a verbal expression for 7a4. A. 7 times a B. 7 times the product of 4 and a C. 7 times a to the fourth power D. 4 times a to the seventh power Example 1 4 B. Write a verbal expression for x2 + 3. A. the sum of 3 and x B. the product of x squared and 3 C. the sum of x and 3 squared D. the sum of x squared and 3 Example 1 Addition Subtraction Multiplication Division More than Less than Product of Quotient Sum Multiplied by Divided by Plus Subtracted from Difference Increased by Added to Decreased by minus Of Times KC 5 Write Algebraic Expressions A. Write an algebraic expression for 5 less than a number c. The words less than suggest subtraction. a number c less five c – 5 Answer: Example 2 Write Algebraic Expressions B. Write an algebraic expression for 9 plus the product of 2 and d. Plus implies add, and product implies multiply. Answer: Example 2 6 Write Algebraic Expressions C. Write an algebraic expression for two fifths of the area a. The word of implies multiply. Example 2 A. Write an algebraic expression for nine more than a number h. A. 9 – h B. 9h C. 9 + h D. h – 9 Example 2 7 B. Write an algebraic expression for the difference of 6 and 4 times a number x. A. 6 – 4x B. (6 – 4) + x C. 6 + 4x D. 6x – 4 Example 2 C. Write an algebraic expression for one half the size of the original perimeter p. A. 2p B. C. p2 D. p Example 2 8 Write an Expression ENTERTAINMENT Mr. Nehru bought two adult tickets and three student tickets for the planetarium show. Write an algebraic expression that represents the cost of the tickets. Let a be the cost of each adult ticket and c be the cost of each student ticket. The cost of the adult tickets is represented by 2a and the cost of the student tickets is represented by 3c. Answer: Example 3 MONEY Lorenzo bought a bag of peanuts that cost p dollars and he gave the cashier a $20 bill. Write an expression for the amount of change that he will receive. A. 20 – p B. p – 20 C. 20 + p D. 20 p Example 3 9 • Homework: Page 7 #’s 16-28 Evens Only 10