Start Learning Now

Our free lessons will get you started (Flash® 10 required).

Algebraic Expressions

• An algebraic expression differs from an open sentence or equation in that it has no equal sign.
• The value of an algebraic expression can vary depending on the value of the variable.
• Within a single problem, the value of the variable remains the same.
• A variable is a symbol that represents one or more numbers. A mathematical expression with one or more variables is an algebraic expression. To evaluate an algebraic expression, replace each variable with a number and then simplify.

• 5 ×(81 ÷9) =
• 5 ×9 =

Evaluate the expression 72 ÷ (y - 62) for x = 70.

• 72 ÷(70 − 62) =
• 72 ÷8 =

• 10(3) − 4 =
• 30 − 4 =

• 24 ÷4 + 9 =
• 6 + 9 =

Evaluate the expression x × 2 + (17 - y) for x = 5 and y = 15.

• 5 ×2 + (17 − 15)=
• 10 + 2 =

The formula A = l × w ÷ 2 gives the area of a right triangle with length l and width w. Find the area of a right triangle with a length of 9 in and a width of 8 in.

• A = 8in ×9in ÷2
• A = 72in2 ÷2

Solve for Q if Q = 63 ÷ j + 7 × k and j = 7,k = 4.

• Q = 63 ÷7 + 7 ×4
• Q = 9 + 28

Eric's store charges \$ 5 for a shake and \$ 4 for a smoothie. How much does he make when a customer buys 3 shakes and 5 smoothies?

• Let x = number of shakes bought. Let y = number of smoothies bought.
• Total = \$5x + \$4y, and x = 3, y = 5.
• Total = \$5(3) + \$4(5)
• Total = \$15 + \$20

Tiffany uses the formula \$ 7m + \$ 3n to calculate her son Jason's allowance, with m = number of As on his report card, and n = number of Bs on his report card. What is Jason's allowance if he received 2 As and 4 Bs?

• \$7m + \$3n, and m = 2, n = 4
• \$ 7(2) + \$ 3(4) =
• \$ 14 + \$ 12 =

R = 10a - 13b + 5c. Find R if a = 10, b = 2, and c = 3.

• R = 10(10) − 13(2) + 5(3)
• R = 100 − 26 + 15
• R = 74 + 15

Let a = number of apples, b = number of bananas, and c = number of carrots. An apple costs 50 cents, a banana costs 85 cents, and a carrot costs 30 cents. a) Find the formula for the total cost of apples, bananas, and carrots. b) How much does 2 apples, 1 banana, and 3 carrots cost?

• a) 50a + 85b + 30c
• b) 50(2) + 85(1) + 30(3) =
• 100 + 85 + 90 =
• 185 + 90 =

275 cents, or \$2.75

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.