Variable Expressions Digital Lesson

Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 2 Definition: Variable These are examples of variable expressions. A variable (or algebraic) expression is an expression formed from numbers and variables by adding, subtracting, multiplying, dividing, taking powers, taking roots, and using grouping symbols.

Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 3 Value Examples: Find the Value of the Variable Expressions Replacing the variables in a variable expression by numbers produces a numerical expression. When this is evaluated the resulting number is the value of the variable expression. Examples: 1. Find the value of 3x – 5 when x = – 1. = 3(– 1) – 5 = – 3 – 5 = – 8 2. Find the value of when x = 4. (4) Replace the variable x with the number – 1. Replace the variable x with the number 4.

Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 4 Verbal Expressions We use variable expressions to represent verbal expressions. Examples of verbal expressions: “4 pizzas less than we served yesterday” “8 times as many nickels as quarters” a = Alice’s age p = number of pizzas served yesterday q = number of quarters n = number of nickels “3 years older than Alice” a + 3 p – 4 n = 8q These can be translated into variable expressions:

Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 5 ( ) 3 Examples: Translation Examples: 1. Write the expression “6 more than x” as a variable expression. Look for keywords in expression. x Identify the variable. + 6“6 more than x” 2. Write “12 decreased by b” as a variable expression. b– 12“b decreased by 12” 3. Write “2 less than a, cubed” as a variable expression. a– 2“2 less than a, cubed” “more than” often indicates an addition. “decreased by” often indicates a subtraction. “less than” often indicates a subtraction.

Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 6 Example: Evaluate Examples: 1. Evaluate “the difference between x and the total of 4 times x and 2” when x = 15. “The difference between x and the total of 4 times x and 2.” Identify parts of the phrase that can be grouped on their own. – 3x – 2 2. Evaluate “the sum of 4 and y, divided by the square root of x” when x = 4 and y = 6. 4x4x + 2 Identify keywords. ( ) x – – 3(15) – 2 Simplify. Evaluate at x = 15. – 47 (6) (4)

Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 7 Examples: Find the Value Division by zero is undefined. Examples: 1. Find the value of the (4x + 3) 2 + |x| when x = – 2. = (4(– 2) + 3) 2 + |(– 2)| = (– 8 + 3) = (– 5) Evaluate when a = 3 and b = – 1. Evaluate expressions within grouping symbols. Simplify the exponent. = (– 5 ) (– 5) + 2 = = 27 Add. (3) (– 1) This expression is undefined when a = 3 and b = – 1.

Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 8 (2) + ((2) 5) Examples: Translate & Evaluate Example: Write a variable expression for “A number plus the product of the number and 5.” Evaluate this expression when “a number” is 2. x “a number plus”“product of the number and 5.” Let x = “a number”. Evaluate when x = 2. +(x 5) (2) Example: Write a variable expression for “There are 6 times as many cars as trucks.” How many trucks are there if there are 12 cars? 6= For every truck there are six cars. Let c = the number of cars and t = the number of trucks. (12) = 6t t = 2 There are 2 trucks. Evaluate when c = 12. ct

Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 9 Application: Volume of a Sphere Variable expression: (1) Example: The volume of a sphere is the product of and its radius cubed. What is the volume of a sphere with a radius of 1 meter? 2 meters? 5 meters? Write the answers in cubic meters. Let V = volume of the sphere, and r = radius. Radius = 1 m: (2) Radius = 2 m: (5) Radius = 5 m:

Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 10 Application: Fahrenheit to Celsius Example: To convert a temperature from Fahrenheit to Celsius, subtract 32 and multiply the result by. Convert 72°F to Celsius, and – 40°C to Fahrenheit. Celsius to Fahrenheit: Let C = Celsius and F = Fahrenheit. Fahrenheit to Celsius: Divide through by, and add 32 to both sides. 72°F to Celsius: (72) – 40°C to Fahrenheit: (– 40)