1. 1.1 Variables in Algebra Algebra 1 Concepts and Skills McDougal LittellLinda 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 numerical expression. A variable expression consists of constants, variables and operations. constants - numbersvariables - letters operations - addition, subtraction, multiplication and division Example 3 + 2

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

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

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

6. When substituting a value into an expression, use parentheses. To evaluate a variable expression, you write the expression, substitute a number for each variable, and simplify. Evaluate the variable expression when b = 3. The problem.7b7b Substitute.7(3) Simplify. 21 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.

7. Example 3 Evaluate 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 4 Evaluate 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 = rate time Distance Perimeter A measure of the distance around a geometric figure. triangle rectangle Area rectangle triangle square units of the interior region of a two dimensional figure or the surface of a three dimensional figure.

10. Example 5 Use a variable expression to find the distance traveled by a truck moving at an average speed of 65 miles per hour for 6 hours. 1.Write the formula. d = rt 2. Substitute. = (65)(6) 3. Simplify. = 390 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 6 Find 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 6 Find 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. What is the name of this triangle according to the angles and the sides? Example 7 Find the area of a triangle with base 15 centimeters and height 8 centimeters. right scalene triangle

14. Example 7 Find 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 square centimeters. cannot You cannot write 60 2 cm. The area of the triangle is 60 cm 2.

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