Study Guide: Algebraic Expressions

Study Guide: Algebraic Expressions

AE1: I can translate a math expression into words

AE2: I can translate words in to a math expression

AE3: I can develop and simplify algebraic expressions for word problems

AE4: I can evaluate algebraic expressions

For each problem below TWO ways you can algebraic expression into words.

For each problem below, write an algebraic expression that matches the given phrase.

1.) 40 increased by the cube of a number2.) 8 less than x

3.) the sum of 20 and a number squared4.) one third the difference of a

number and 30

5.) the product of a number and 11, decreased by 126.) the quotient of 12 and a number

For each of the following word problems, set up an expression based on the situation. Then, simplify the expression as much as possible.

1. Nancy and Bill collect coins. Nancy has x coins. Bill has six more than twice the number that Nancy has. Write and simplify an expression for the total number of coins Bill and Nancy have together.

2. Gabe goes to the mall. If x is the number of items he bought, then the expression 20x – 6 gives the amount he spent in dollars at one store. Then he spent three less than three times x at another store. Write and simplify and expression that represents the total amount Gabe spent at the mall.

3. An art class is making a mural for their school which has a triangle drawn in the middle. The length of the bottom of the triangle is three less than the square of x. A second side is 5 more than the product of 4 and a number. The last side is 5more than the cube of a number. Write and simplify an expression for the perimeter of the triangle.

4. A company has two manufacturing plants with daily production levels. Plant #1’s production levels are 10 more than four times x. Plant #2’s production levels are the difference between seven times x and three. Write and simplify an expression to represent how much more plant 1 produces than plant 2.

5. Two friends are shopping for vegetables. Mary buys a box of tomatoes for $5.25 and 4 pounds of green beans. Morris buys a large bag of corn for $7.00 and 2 pounds of green beans. Use the variable “p” to represent the price, in dollars, per pound of green beans. Write and simplify an expression to represent how much more Morris spent.

6. Meyrick has a box with DVD’s and Wii games in it. The number of DVD’s is 10 less than the product of four and a number. The total number of DVd’s and Wii games in the bag is 15 more than the square of a number. Write and simplify an expression that represents the number of Wii games in the box.

Evaluate each of the following expressions using the given values for the variables.

Show all work!

x = -1 y = 5 z = -7 a = -6 b = -2 c = 4

1. 4xyz2. 6b +2c3. ab

c

4. x2y – 105. a/26. a + b +c + x + y + z