1. Algebraic Expressions and Terms
Unit 1

2. Objective The student will be able to:
translate verbal expressions into math expressions and vice versa.

3. You are familiar with the following type of numerical expressions:
3 (12)
6 ( )
(6)

4. What is a variable?
In the expression B, the letter “B” is a variable.
A variable is a letter or symbol that represents an unknown value.

5. What is the area of a rectangle?
Length times Width
If the length is 3 meters and the width is 2 meters, what is the area?
A = L x W A = 3 x 2 = 6 meters2
A, L and W are the variables. It is any letter that represents an unknown number.

6. Algebraic Expressions
When variables are used with other numbers, parentheses, or operations, they create an algebraic expression.
a + 2
(a) (b)
3m + 6n - 6

7. What are coefficients?
A coefficient is the number multiplied by the variable in an algebraic expression.
Algebraic Expression Coefficient 6m
8r + 7m , 7
14b

8. What is a term?
A term is the name given to a number, a variable, or a number and a variable combined by multiplication or division.
Algebraic Expressions Terms
a a, 2
3m + 6n m, 6n, - 6

9. What are constants?
A constant is a number that cannot change its value.
In the expression: 5x + 7y - 2
the constant is - 2.

10. Identify the terms, coefficients, and constants.
Figure it out!
Identify the terms, coefficients, and constants.
1. 12a - 6b + 4
2. 4x - 2y
3. c
4. 3x + 2

11. Writing Algebraic Expressions

12. An algebraic expression contains:
1) one or more numbers or variables, and
2) one or more arithmetic operations.
Examples:
x - 3
3 • 2n

13. In expressions, there are many different ways to write multiplication.
1) ab
2) a • b
3) a(b) or (a)b
4) (a)(b)
5) a x b
We are not going to use the multiplication symbol any more. Why?

14. Division, on the other hand, is written as:1)
2) x ÷ 3

15. Throughout this year, you will hear many words that mean addition, subtraction, multiplication, and division. Complete the table with as many as you know.

16. Addition Phrases: More than Increase by Greater than Add Total Plus
Sum

17. Subtraction Phrases: Decreased by Difference between Take Away Less
Less than*
Subtract from*
Minus

18. Multiplication Phrases:
Product
Times
Multiply Of
Twice or double
Triple

19. Division Phrases:
Quotient
Divide
Divided by
Split equally
Ratio

20. Write an algebraic expression for 1) m increased by 5.
2) 7 times the product of x and t.
7xt or 7(x)(t) or 7 • x • t

21. 3) 11 less than 4 times a number.
4) two more than 6 times a number.
6n + 2
5) the quotient of a number and 12.

22. Which of the following expressions represents 7 times a number decreased by 13?
Answer Now

23. Which one of the following expressions represents 28 less than three times a number?
Answer Now

24. Write a verbal expression for: 1) 8 + a.
The sum of 8 and a 2)
The ratio of m to r
Do you have a different way of writing these?

25. Which of the following verbal expressions represents 2x + 9?
9 increased by twice a number
a number increased by nine
twice a number decreased by 9
9 less than twice a number
Answer Now

26. Which of the following expressions represents the sum of 16 and five times a number?
Answer Now

27. When looking at the expression 103, 10 is called the
base
and 3 is called the
exponent or power.
103 means 10 • 10 • 10
103 = 1000

28. How is it said? 21 Two to the first power 22
Two to the second power or two squared 23
Two to the third power or two cubed
2n7
Two times n to the seventh power

29. Which of the following verbal expressions represents x2 + 2x?
the sum of a number squared and twice a number
the sum of a number and twice the number
twice a number less than the number squared
the sum of a number and twice the number squared
Answer Now

30. Which of the following expressions represents four less than the cube of a number?
Answer Now

31. We can’t evaluate because we don’t know what n equals to!!2 22
2 • 2 = 4 23
2 • 2 • 2 = 8
2n7
We can’t evaluate because we don’t know what n equals to!!

32. Is 35 the same as 53? Evaluate each and find out!
35 = 3 • 3 • 3 • 3 • 3 = 243
53 = 5 • 5 • 5 = 125
243 ≠ 125
They are not the same!

33. Write algebraic expressions for these word phrases
Four more than s
The product of 7 and c
Nine less than x
A number divided by the sum of 4 and 7.
Twice the sum of a number plus 4.
The sum of ¾ of a number and 7.
Ten times a number increased by 150.

34. Write an algebraic phrase for these situations
A car was traveling 35 miles per hour for a number of hours.
Bob ran 7 times a week for a number of weeks.
The plumber added an extra $35 to her bill.
Thirty-five fewer people came than the number expected.

35. Video links