## Algebraic expressions: Section 2Question 5. What do we mean by the value of a letter?
The value of a letter is a Question 6. What does it mean to evaluate an expression? It means to replace each letter with its value, and then do the order of operations.
Example 6. Let
In each case, copy the pattern. Copy the + signs and copy the parentheses ( ). When you come to
Problem 7. Let
g) Again, 100 − 16 + 12 does
That is 168 divided by 100. See Lesson 4 of Arithmetic, Question 4. Question 7. Why is a literal symbol -- Because its A variable, such as Numerical symbols -- 2, 3, 4 -- are called constants. The value of those symbols does not vary. (See Constants versus variables.)
Problem 8. Two variables. Let the value of the variable
Calculate the value of When When When When When Algebraic expressions Real problems in science or in business occur in ordinary language. To do such problems, we typically have to translate them into algebraic language.
Problem 9. Write an a) Six times a certain number.
6 b) Six more than a certain number.
c) Six less than a certain number.
d) Six minus a certain number.
6 − e) A number repeated as a factor three times.
f) A number repeated as a term three times.
g) The sum of three consecutive whole numbers. The h) Eight less than twice a certain number.
2 i) One more than three times a certain number.
3 Now an algebraic Problem 10. Write each statement algebraically. a) The sum of two numbers is twenty.
b) The difference of two numbers is twenty.
c) The product of two numbers is twenty.
d) Twice the product of two numbers is twenty.
2 e) The quotient of two numbers is equal to the sum of those numbers.
Formulas A formula is an algebraic rule for evaluating some quantity. A formula is a statement. Example 7. Here is the formula for the area
"The area of a rectangle is equal to the base times the height." And here is the formula for its perimeter
"The perimeter of a rectangle is equal to two times the base For, in a rectangle the opposite sides are equal.
Problem 11. Evaluate the formulas for
Problem 12. The area
Find
When 1 cm is the unit of length, then 1 cm² ("1 square centimeter") is the unit of area. Problem 13. The formula for changing temperature in degrees Fahrenheit (F) to degrees Celsius (C) is given by this formula:
Find C if F = 68°. Replace F with 68:
" Next Lesson: Signed numbers -- Positive and negative Copyright © 2021 Lawrence Spector Questions or comments? E-mail: [email protected] |