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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.

Algebraic Expressions

Evaluate the expression 5 × (81 ÷ x) for x = 9.
• 5 ×(81 ÷9) =
• 5 ×9 =
45
Evaluate the expression 72 ÷ (y - 62) for x = 70.
• 72 ÷(70 − 62) =
• 72 ÷8 =
9
Evaluate the expression 10m - 4 when m = 3.
• 10(3) − 4 =
• 30 − 4 =
26
Evaluate the expression n ÷ 4 + 9 when n = 24.
• 24 ÷4 + 9 =
• 6 + 9 =
15
Evaluate the expression x × 2 + (17 - y) for x = 5 and y = 15.
• 5 ×2 + (17 − 15)=
• 10 + 2 =
12
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
A = 36in2
Solve for Q if Q = 63 ÷ j + 7 × k and j = 7,k = 4.
• Q = 63 ÷7 + 7 ×4
• Q = 9 + 28
Q = 37
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
Total = \$35
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 =
\$26
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
R = 89
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.

Algebraic Expressions

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

• Intro 0:00
• What You'll Learn and Why 0:05
• Topics Overview
• Vocabulary 0:16
• Variable
• Algebraic Expression
• Evaluate
• Modeling an Algebraic Expression 1:16
• Model the Expression 2x + 4
• Evaluating an Algebraic Expression 1:47
• Evaluate 3x - 7 for x = 8.2
• Evaluating an Algebraic Expression 2:45
• Evaluate (3.7 + x) ÷ 2 for x = 9.6
• Using a Table to Evaluate an Expression 4:10
• Example: Pairs of Shoes
• Extra Example 1: Evaluate the Expression 5:46
• Extra Example 2: Evaluate the Expression 6:06
• Extra Example 3: Perimeter of a Rectangle 6:46
• Extra Example 4: Finding Income 7:40