Algebraic Expressions and Terms Unit 1

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

You are familiar with the following type of numerical expressions: 12 + 6 3 (12) 6 (3 + 2) 15 - 4 (6)

What is a variable? In the expression 12 + B, the letter “B” is a variable. A variable is a letter or symbol that represents an unknown value.

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.

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

What are coefficients? A coefficient is the number multiplied by the variable in an algebraic expression. Algebraic Expression Coefficient 6m + 5 6 8r + 7m + 4 8, 7 14b - 8 14

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 + 2 a, 2 3m + 6n - 6 3m, 6n, - 6

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

Identify the terms, coefficients, and constants. Figure it out! Identify the terms, coefficients, and constants. 1. 12a - 6b + 4 2. 4x - 2y 3. c - 32 4. 3x + 2

Writing Algebraic Expressions  

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

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?

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

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

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

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

Multiplication Phrases: Product Times Multiply Of Twice or double Triple

Division Phrases: Quotient Divide Divided by Split equally Ratio

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

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.

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

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

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?

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

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

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

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

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

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

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!!

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!

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.

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.

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