1. Algebraic Expressions Honors Math – Grade 8

2. Get ready for the Lesson Alana works at a beach arcade during summer vacation. Her salary is $7.25 an hours plus a one-time bonus of $75. What algebraic expression represents how much Alana will earn over the summer? An algebraic expression is a mathematical expression consisting of numbers, variables and operations.. A variable is a symbol, usually a letter, representing one or more numbers. To write an algebraic expression 1.Define a variable for the unknown. 2.Write an expression in terms of the same variable for any other unknown quantities.

3. A term of an algebraic expression is a number, a variable or a product or quotient of numbers and variables. 4 terms The numerical part of a term that contains variables is the numerical coefficient. Numerical coefficient The variable, or variables, of a term is called the literal coefficient. Literal coefficient A term that does not have variables is called a constant. Name the coefficient.

4. To write an algebraic expression, you must be able to determine the mathematical operation(s) associated with word phrases. Addition a + b a plus b The sum of a and b a and b are added a is increased by b b is added to a b more than a the number that exceeds a by b Subtraction a – b a minus b The difference between a and b b subtracted from a a decreased by b a diminished by b b less than a a reduced by b Multiplication a b, a x b, (a)(b), a(b) a times b the product of a and b b multiplied by a Division a divided by b The quotient of a and b

5. Write an algebraic expression for each verbal expression. Verbal ExpressionAlgebraic Expression Key Words The number of minutes, m, increased by 10 Increased bysuggests addition. 28 subtracted from y Subtracted from suggests subtraction. The variable is already defined. Twice the number of apples, a Twice implies multiplication. The variable is already defined. The number of girls, g, divided by 5 Divided by suggests division. The variable is already defined. Algebraic expressions may contain more than one operation and may involve the use of grouping symbols. Let’s take a closer look!

6. Write an algebraic expression for each verbal expression. Verbal ExpressionAlgebraic Expression Key Words 38 diminished by the absolute value of the product of 7 and number Diminished by suggests subtraction Product suggests multiplication 11 more than one fourth of a number. More than suggests subtraction. Of suggest multiplication Define a variable. 10 times the difference of 15 and a number Times implies multiplication. Difference suggests subtraction Define a variable. 2 times the quantity 8 plus n squared. Times suggests division. Squared suggests an exponent. The variable is already defined. Define a variable. The sum of the opposite of a number and 12 divided by 9 Sum suggests addition. Opposite of a number Divided by suggests division Define a variable.

7. Write an algebraic expression for each verbal expression. The value in cents of d dimes and n nickels. Not all word phrases translate directly into algebraic expressions. Sometimes you need to interpret a situation and apply a familiar fact. The value of 1 dime is 10 cents, so the value of d dimes is 10d cents. The value of 1 nickel is 5 cents, so the value of n nickels is 5n cents. The word total indicates addition, so the total value in cents is…

8. To evaluate an algebraic expression, you substitute numbers for the variables in the expression and then compute using the Order of Operations. KEY CONCEPT The Substitution Principle For any numbers a and b, if a = b, then a may be replaced with b. THINK… PLUG IT IN!

9. Evaluate the following expressions when d = 5000 Substitute 5000 for d. Then simplify using the Order of Operations.

10. Evaluate the following expressions when t=40, u=120, v=100, and w=75 Substitute: 100 for v 75 for w Simplify using the order of operations. Substitute: 100 for v 75 for w 50 for t