8th Grade Math Lesson 2-10 Practice
Vocabulary Terms Define/Illustrate
1. Formula
2. Rearrange an equation
3. Variables
Problems: Show all work: Solve for each of the formulas for the indicated variable(s)
4. P=2L+2W for W
5. AX+B=0 for X
6.V+LWH for H
7. Y=MX+B for X
8. If the perimeter of a rectangle is 60ft and its length is 18ft, find its width. (see formula in number 1)
1. Formula: A mathematical equation or relationship that expresses a rule or principle. (illustration: E = mc^2, where E represents energy, m represents mass, and c represents the speed of light)
2. Rearrange an equation: To manipulate an equation to isolate a specific variable or term. (illustration: rearranging the equation 2x + 3 = 7 to solve for x by subtracting 3 from both sides and then dividing by 2)
3. Variables: Symbols used to represent unknown values or quantities in mathematical expressions or equations. (illustration: x, y, a, b, etc.)
4. P = 2L + 2W for W:
To solve for W, we need to isolate it on one side of the equation:
P - 2L = 2W
Divide both sides by 2 to solve for W:
(P - 2L) / 2 = W
5. AX + B = 0 for X:
To solve for X, we need to isolate it on one side of the equation:
AX = -B
Divide both sides by A to solve for X:
X = -B/A
6. V + LWH for H:
To solve for H, we need to isolate it on one side of the equation:
LWH = H - V
Divide both sides by LW to solve for H:
H = (LWH - V) / LW
7. Y = MX + B for X:
To solve for X, we need to isolate it on one side of the equation:
MX = Y - B
Divide both sides by M to solve for X:
X = (Y - B) / M
8. If the perimeter of a rectangle is 60ft and its length is 18ft, find its width:
The formula for the perimeter of a rectangle is P = 2L + 2W.
We are given that the perimeter is 60ft and the length is 18ft, so we can substitute those values into the formula:
60 = 2(18) + 2W
Simplify and solve for W:
60 = 36 + 2W
Subtract 36 from both sides:
24 = 2W
Divide both sides by 2 to solve for W:
W = 12ft
Vocabulary Terms:
1. Formula: A mathematical expression representing a relationship between variables. It allows us to derive a particular value or solve for a specific variable in an equation.
Illustration: One example of a formula is the area of a rectangle, A = l * w, where A represents the area, l represents the length, and w represents the width.
2. Rearrange an equation: To rearrange an equation means to manipulate it algebraically in order to isolate a specific variable. This allows us to solve for that variable.
Illustration: For example, if we have the equation 2x + 3 = 9, we can rearrange it by subtracting 3 from both sides to isolate the term with x: 2x = 6.
3. Variables: Symbols or letters that represent unknown quantities or values in mathematical expressions or equations.
Illustration: In the equation 3x + 4y = 12, x and y are variables representing unknown values.
Problems:
4. P = 2L + 2W for W:
To solve for W, we need to isolate the variable W on one side of the equation.
Rearrange the equation: P - 2L = 2W.
Divide both sides by 2: (P - 2L)/2 = W.
5. AX + B = 0 for X:
To solve for X, we need to isolate the variable X on one side of the equation.
Rearrange the equation: AX = -B.
Divide both sides by A: X = -B/A.
6. V + LWH for H:
To solve for H, we need to isolate the variable H on one side of the equation.
Rearrange the equation: LWH = V.
Divide both sides by LW: H = V/(LW).
7. Y = MX + B for X:
To solve for X, we need to isolate the variable X on one side of the equation.
Rearrange the equation: MX = Y - B.
Divide both sides by M: X = (Y - B)/M.
8. If the perimeter of a rectangle is 60 ft and its length is 18 ft, find its width (using the formula in number 1):
From the formula P = 2L + 2W, we substitute the given values:
60 = 2(18) + 2W.
Simplify: 60 = 36 + 2W.
Subtract 36 from both sides: 24 = 2W.
Divide both sides by 2: W = 12 ft.