Rearranging Equations: Solve for Variables in Math

1. If the formula for the area of a rectangle is A = l * w, how would you rearrange the equation to solve for w?

• w = A - l

• w = A * l

• w = A + l

• w = A / l

2. The formula for the distance traveled is d = rt, where r is the rate and t is the time. If you know the distance and the rate, how can you rearrange the equation to find the time?

• t = d + r

• t = d - r

• t = d/r

• t = r/d

3. A car's fuel efficiency is given by the equation E = d/f, where E is efficiency, d is distance, and f is fuel used. How would you solve for d in terms of E and f?

• d = E / f

• d = E + f

• d = E * f

• d = E - f

4. The formula for the perimeter of a triangle is P = a + b + c. If you know the perimeter and the lengths of two sides, how can you rearrange the equation to find the length of the third side?

• c = P / (a + b)

• c = P + a + b

• c = P - a - b

• c = a - b + P

5. The equation for the volume of a cylinder is V = πr²h. If you want to find the height h in terms of V and r, how would you rearrange the equation?

• h = V / (2πr)

• h = V / (πr)

• h = V / (πr³)

• h = V / (πr²)

6. The formula for the speed of an object is s = d/t. If you know the distance and speed, how can you rearrange the equation to find the time t?

• t = d/s

• t = d - s

• t = d + s

• t = s/d

7. The equation for the total cost C of buying x items at a price p each is C = px. How would you solve for p in terms of C and x?

• p = C + x

• p = C/x

• p = C - x

• p = C * x

8. The formula for the circumference of a circle is C = 2πr. If you want to find the radius r in terms of C, how would you rearrange the equation?

• r = C / π

• r = C / (2π)

• r = C / 4π

• r = C / (π^2)

9. The equation for the area of a triangle is A = 1/2 * b * h. If you know the area and the base, how can you rearrange the equation to find the height h?

• h = A / (1/2 * b)

• h = b / (2 * A)

• h = 2 * A + b

• h = (2 * A) / b

10. The formula for the simple interest I is I = Prt, where P is the principal, r is the rate, and t is the time. How would you solve for r in terms of I, P, and t?

• r = I + (Pt)

• r = I / (Pt^2)

• r = I / (Pt)

• r = I * (Pt)