Digital Lesson Variable Expressions These are examples of
Digital Lesson Variable Expressions
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. 2
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 3 x – 5 when x = – 1. = 3(– 1) – 5 Replace the variable x with the number – 1. = – 3 – 5 Value = – 8 2. Find the value of when x = 4. (4) Replace the variable x with the number 4. Value Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 3
We use variable expressions to represent verbal expressions. Examples of verbal expressions: These can be translated into variable expressions: “ 3 years older than Alice” a+3 a = Alice’s age “ 4 pizzas less than we served yesterday” p– 4 p = number of pizzas served yesterday “ 8 times as many nickels as quarters” n = 8 q q = number of quarters n = number of nickels Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 4
Examples: 1. Write the expression “ 6 more than x” as a variable expression. “ 6 more than x” x + 6 Identify the variable. “more than” often indicates an addition. Look for keywords in expression. 2. Write “ 12 decreased by b” as a variable expression. “b decreased by 12” b – 12 “decreased by” often indicates a subtraction. 3. Write “ 2 less than a, cubed” as a variable expression. “ 2 less than a, cubed” (a – 2 )3 “less than” often indicates a subtraction. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 5
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 keywords. Identify parts of the phrase that can be grouped on their own. x – ( 4 x + 2 ) – 3 x – 2 Simplify. – 3(15) – 2 Evaluate at x = 15. – 47 2. Evaluate “the sum of 4 and y, divided by the square root of x” when x = 4 and y = 6. (6) (4) Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 6
Examples: 1. Find the value of the (4 x + 3)2 + |x| when x = – 2. = (4(– 2) + 3)2 + |(– 2)| = (– 8 + 3)2 + 2 = (– 5 ) • (– 5) + 2 = 25 + 2 = 27 2. Evaluate expressions within grouping symbols. Simplify the exponent. Add. when a = 3 and b = – 1. (3) (– 1) Division by zero is undefined. (3) This expression is undefined when a = 3 and b = – 1. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 7
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 + (x • 5) Let x = “a number”. “a number plus” “product of the number and 5. ” (2) + ((2) • 5) Evaluate when x = 2. (2) + 10 12 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? Let c = the number of cars c = 6 t and t = the number of trucks. (12) = 6 t t=2 Copyright © by Houghton Mifflin Company, Inc. All rights reserved. For every truck there are six cars. Evaluate when c = 12. There are 2 trucks. 8
Example: The volume of a sphere is the product of radius cubed. and its 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. Variable expression: Radius = 1 m: (1) Radius = 2 m: (2) Radius = 5 m: (5) Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 9
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 to Celsius: Divide through by , and add 32 to both sides. 72°F to Celsius: (72) Copyright © by Houghton Mifflin Company, Inc. All rights reserved. – 40°C to Fahrenheit: (– 40) 10
- Slides: 10