Lesson 1 1 Variables and Expressions Warm Up

Lesson 1 -1 Variables and Expressions Warm Up: Paige has exactly $5. 60 in quarter, dimes, and nickels. How many of each coin does Paige have if she has the exact same number of each type of coin?

Variables Vocabulary � ___________ are symbols used to represent unspecified number or values. Any__ letter may be used as a variable. Variable expressions � ____________________ consist of one or more numbers, at least one _________ variable and one or more arithmetic operations. raised dot � Multiplication is shown with a _______ [ 5 ● 6 ], parentheses _________ [ (5)(6) or 5 (6)]. If the factors are a constant (number) and a variable or two no symbol is needed. [ 3 x means 3 times variables, _____ x. ] � In an expression, the quantities being multiplied are called factors ______. And the result is called the product _______

Writing Algebraic Expressions Phrase More than Operation Add (+) Verbal Expression Algebraic Expression 5 more than a number a+5 A number less ten b – 10 Less Subtract (-) Less than Subtract (-) $8 less than Sue Product Multiply (*) The product of 4 and a number x Quotient Divide (÷) The quotient of a number and 6 Difference Subtract (-) The difference of a number x and y Sum Add (+) The sum of 6 and a number S– 8 or 5 +a * notice the order 4 x x–y 6+n **The word “THAN” usually means you have to switch the order. **

Writing expressions with 2 operations How would you rewrite each of these verbal expressions as an algebraic expression? A. 3 more than twice a number 3 + 2 n or 2 n + 3 B. 9 less than the quotient of 6 and a number x C. The product of 4 and the sum of a number x and 7. 4 (x + 7) (you need parentheses because it is 4 times the “SUM”)

Using Words for An Expression D. E. What word phrase can you use to represent each algebraic expression below? 3 x Three times “X” OR The product of 3 and a number “x” 5 x – 1 5 times x minus 1 OR 1 less than 5 times x OR The product of 5 and a number “x” decreased by 1

Practice Try each of the following on your own. Write an algebraic expression for each verbal expression. 1. 2. 3. 4. 5. 6. 7. five less than a number 9 plus the product of 2 and the number d two-thirds of the original volume 24 less than three times a number the sum of 35 and z the product of 16 and p 49 increased by twice a number

8. Bria is saving to buy a new computer. Write an expression to represent the amount of money she will have if she has s dollars saved and she adds d dollars per week for the next 12 weeks. 9. the product of and a to the seventh power 10. the sum of 11 and x to the third 11. 8 less than the product of a number x and 4 12. twice the sum of a number x and 8 13. the quotient of 5 and the sum of 12 and a number x

II. What word phrase can you use to represent the algebraic expression? 14. x + 8. 1 15. 10 x + 9 16.