1.1 Variables in Algebra

1. 1.1 Variables in Algebra Algebra 1 Concepts and Skills McDougal Littell Linda Stamper

2. In Algebra, you can use letters to represent one or more variables. When a letter is used to represent a range of numbers, it is called a variable. The numbers are called values of the variable. An expression that represents a particular number is called a numericalexpression. Example3 + 2 A variableexpression consists of constants, variables and operations. constants - numbers variables - letters operations - addition, subtraction, multiplication and division

3. State the meaning of the variable expression and name the operation. The problem. 16m State the meaning. 16times m Word form multiplication Name the operation. The multiplication symbol x is usually not used in algebra because of its possible confusion with the variable x.

4. Example 1State the meaning of the variable expression and name the operation. 1. Write the problem. 2. State the meaning. k divided by 4 Word form division 3. Name the operation.

5. Example 2State the meaning of the variable expression and name the operation. 1. Write the problem. y– 12 y minus 12 2. State the meaning. 12 subtracted from y 3. Name the operation. 12 less than y subtraction

6. To evaluate a variable expression, you write the expression, substitute a number for each variable, and simplify. Evaluate the variable expression when b = 3. In algebra work downward in columns. Skip one line after the answer. Highlight or circle your answer. You may find it helpful to fold your paper in half lengthwise to create 2 columns. The problem. 7b Substitute. 7(3) 21 Simplify. When substituting a value into an expression, use parentheses.

7. Example 3Evaluate the variable expression when b = 3. 1. Write the problem. 2. Substitute. 3. Simplify. 6 Get into the habit of using parentheses when you substitute. It will help eliminate errors when the problems are more complex!

8. Example 4Evaluate the variable expression when b = 3. 1. Write the problem. 2. Substitute. 3. Simplify. 9

9. A formula is an algebraic equation that relates two or more quantities. Distance distance = rate • time Perimeter triangle A measure of the distance around a geometric figure. rectangle Area rectangle square units of the interior region of a two dimensional figure or the surface of a three dimensional figure. triangle

10. Example 5Use a variable expression to find the distance traveled by a truck moving at an average speed of 65 miles per hour for 6 hours. d = rt 1.Write the formula. = (65)(6) 2. Substitute. = 390 3. Simplify. 4. Write a sentence. The truck traveled 390 miles. Note: Include the label in your sentence. Use one equal sign per line of work. Keep the equal signs in a line!

11. Example 6Find the perimeter of a triangle with two sides 5 miles long and one side 3 miles long. What is the name of this triangle according to the angles and the sides? acute isosceles triangle

12. Example 6Find the perimeter of a triangle with two sides 5 miles long and one side 3 miles long. 1. Write the formula. P = a + b +c 2. Substitute. = (5) + (5) + (3) 3. Simplify. = 13 4. Write a sentence. The triangle has a perimeter of 13 miles. Check if you used one equal sign per line of work. Are the equal signs in a line?

13. Example 7Find the area of a triangle with base 15 centimeters and height 8 centimeters. What is the name of this triangle according to the angles and the sides? right scalene triangle

14. Example 7Find the area of a triangle with base 15 centimeters and height 8 centimeters. 1. Write the formula. 2. Substitute. 3. Simplify. = 60 4. Write a sentence. The area of the triangle is 60 squarecentimeters. The area of the triangle is 60 cm2. You cannot write602cm.

15. Homework 1-A1 Pages 6-7, #17-46