Algebraic Expressions
In the example below, identify the following parts:
Terms, Coefficients, and Constants
5x + 3
Terms: 5x, 3
Coefficients: 5
Constants: 3
Write the phrase as an expression:
the product of 4 and 17
4 x 17
Tell which property the statement illustrates:
3.5 * w = w * 3.5
Communicative Property of Multiplication
Use the Distributive Property to find the product of:
7 x 86
7(80) + 7(6)
560 + 42
602
Complete the table:
x x + 5
1
3
5
1 + 5 = 6
3 + 5 = 8
5 + 5 = 10
In the example below, explain the following parts:
Terms, Coefficients, and Constants
8x + 2x + 3 + 9
Terms: 8x, 2x, 3, 9
Coefficients: 8, 2
Constants: 3, 9
12 subtracted from a number x
x - 12
Tell which property the statement illustrates:
15 + (22 + w) = (15 + 22) + w
Associative Property of Addition
Use the Distributive Property to find the product of:
5 (w - 8)
5(w) - 5(8)
5w - 40
Evaluate the expression when a=8 and b=2.
a2 - 6 + b
64 - 6 + 2
58 + 2
60
Evaluate k + 15 when k=22
37
Write the phrase as an expression. Then evaluate when x=3 and y=7:
the sum of a number x and 4, then divided by y
(x + 4) / y
(3 + 4) / 7
7 / 7
1
Simplify the expression. Explain each step.
3.2 + (b + 5.7)
3.2 + (b + 5.7) = (3.2 + 5.7) + b
Associative Property of Addition
8.9 + b
Combine Like Terms
Simplify the expression:
4w + 3(w - 2)
4w + 3(w) - 3(2)
4w + 3w - 6
7w - 6
The expression 15a + 12c is the cost (in dollars) of admission at an amusement park for "a" adults and "c" children. Find the total cost for 5 adults and 10 children.
15(5) + 12(10)
75 + 120
$195
Evaluate 6x + 2 when x=4
26
Write the phrase as an expression. Then evaluate when x=3 and y=7:
6 more than the product of 8 and a number x
8(x) + 6
8(3) + 6
24 + 6
30
Simplify the expression. Explain each step.
6 * (10 * k)
6 * (10 * k) = (6 * 10) * k
Associative Property of Multiplication
60k
Multiplication
Factor the expression using the GCF:
12 + 21
3(4 + 7)
To rent a moving truck for the day, it costs $50 plus $2 for each mile driven. First, write an expression for the cost to rent the truck. Then, how much do you pay in total when you drive the truck 300 miles?
50 + 2x
50 + 2(300)
50 + 600
$650
Evaluate the expression when a=4 and b=0.5
2a + 2b
2(4) + 2(0.5)
8 + 1
9
Write the phrase as an expression. Then evaluate when x=3 and y=7:
the quotient of 40 and the difference of y and 2
40 / (y - 2)
40 / (7 - 2)
40 / (5)
8
The expression 18 + 7 + (18 + 2x) + 7 represents the perimeter of a trapezoid. Simplify the expression.
2x + 50
Factor the expression using the GCF:
16x - 36
4(4x - 9)
You make party favors for an event. You tie 6 inches of ribbon around each party favor. First, write an expression for the amount of ribbon you need for "n" party favors.
Now, the ribbon costs $3 for each foot. Write an expression for the total cost of the ribbon.
6n
3*(0.5n)