1. Chapter 01 – Section 01 Variables and Expressions

2. © William James Calhoun To translate verbal expressions into mathematical expressions and vice versa. This section is the basics of the basics. Terms to become familiar with: variables – symbol used to express an unspecified number algebraic expressions – one or more numbers and variables along with one or more arithmetic operations factors – quantities that are being multiplied product – the result of factors being multiplied

3. © William James Calhoun EXAMPLE 1α: Write an algebraic expression for each verbal expression. a. three times a number x subtracted from 24 b. 5 greater than half of a number t

4. © William James Calhoun EXAMPLE 1β: Write an algebraic expression for each verbal expression. a. m increased by 5 b. the difference of x and 9 c. 7 times the product of x and t

5. © William James Calhoun EXAMPLE 2α: Write a verbal expression for each algebraic expression. a. (3 + b) ÷ y b. 5y + 10x

6. © William James Calhoun EXAMPLE 2β: Write a verbal expression for each algebraic expression. a. 9t b. 8 + a c. 7 – 3y

7. © William James Calhoun More terms you will need to become familiar with: power – an expression with a superscript representing a number multiplied by itself a certain number of times Examples of powers: 5 4 and x 3 base – the number or variable that is multiplied exponent – the superscript number that signifies the number of times multiplication should occur 4 5 = 4 * 4 * 4 * 4 * 4 four is multiplied by itself five times { = 1024

8. © William James Calhoun EXAMPLE 3α: Write a power that represents the number of smallest squares in the large square. Count the number of squares along one side. There are 8 squares in each row. Count the number of squares along the other side. There are 8 squares in each column. To find the number of smallest squares, you would multiply 8 * 8. 8 * 8 can be written as a power by 1) writing the base, 8, once 2) writing the number of times multiplied, 2, once superscripted Answer: 8 2

9. © William James Calhoun EXAMPLE 3β: Write a power that represents the number of smallest squares in the large square.

10. © William James Calhoun EXAMPLE 4α: Evaluate 3 4. Method 1 Write the problem out in long form. 3 * 3 * 3 * 3 Multiply in small steps. 3 * 3 = 9 9 * 3 = 27 27 * 3 = 81 Method 2 Use your calculator. Hit the “3” key. Hit the power key – “^” or “y x ”. Hit the “4” key. Hit the “=“ key. Answer: 81.

11. © William James Calhoun EXAMPLE 4β: Evaluate each expression. a. 3 5 b. 5 3

12. © William James Calhoun PAGE 8 #15 – 39 odd