: Algebra I Lesson 1.1 Variables in Algebra
: Goal 1: Evaluating Variable Expressions A variable is a letter that is used to represent one or more numbers. The numbers are the values of the variable. A variable expression is a collection of numbers, variables, and operations.
: Examples Variable Expression Meaning Operation 8y 8(y) 8 times y Multiplication 16 ------- 16/b 16 divided by b Division b 4 + s 4 plus s Addition 9 - x 9 minus x Subtraction
: Evaluating the Variable Expression The expression 8y is usually not written as 8 x y because of possible confusion of the variable x. Replacing each variable in an expression by a number is called evaluating the variable expression. The resulting number is the value of the expression. Write the variable Substitute values expression. for variables. Simplify the numerical expression.
: Examples (con.) Evaluate the expression when y = 2. a. 8y = 8(2) =16 b. 10 10 ---- = ----- y 2 = 5 Substitute 2 for y.Simplify. Substitute 2 for y. Simplify.
: Evaluating a Real-Life Expression Average speed is given by the following formula. d DistanceAverage speed = --- = -------------- t Time
: Examples (con.) Find the average speed (in mph) of a car that traveled 180 miles from Boise, Idaho, to the Minidoka National Wildlife Refuge in 3 hours. dAverage Speed = ---- Write expression. t = 180 ------ Substitute 180 for d & 3 3 for t. = 60 Simplify.
: Evaluating a Geometric Expression The perimeter of a triangle is equal to the sum of the lengths of its sides: a + b + c. Find the perimeter of the triangle. The dimensions are in feet. a = 8, b = 15, c = 17. Perimeter = a + b + c Write expression. = 8 + 15 + 17 Substitute values. = 40 Simplify.
: Evaluating Simple Interest The simple interest earned by money P (called the principal) at an annual interest rate r for t years is given by Prt. You deposit $650 at a rate of 8% per year. How much simple interest will you earn after one half of a year? Simple Interest (SI) = Prt Write expression. = (650)(0.08)(0.5) Substitute values. = 26 Simplify.After one half of a year, you will have $26 of SI.
: Goal 2: Modeling A Real-Life Situation Writing the units of each variable in a real-life problem helps you determine the units for the answer. This is called unit analysis and it is often used in problem solving for science. When the same units of measure occur in the numerator and the denominator of an expression, you can cancel the units. In real-life problems, you may need to translate words into mathematics. One way to do this is to use a verbal model.
: Finding Time You plan to go hiking in the Jedidiah Smith Redwoods State Park in California. You estimate you'll hike at a rate of 2 miles per hour on a steep trail. Let's say the distance is about 7.4 miles. How long will it take you to hike from Howland Hill Road along the Boy Scout Tree Trail and back? DistanceVerbal Model- Time = -------------- Rate
: Finding Time (con.) Labels- Time = t (hours) Distance = 7.4 (miles) Rate = 2 (mph) Algebraic Model- t = 7.4 ------- 2 = 3.7 It should take you about 3.7 hrs to hike the trail.
: Using Unit Analysis Use unit analysis to check that hours are the units of the solution. Distance mi hTime = ------------- = ------- = mi ----- = h Rate mi/h mi