Mastering Equation Manipulation

Let's explore the fascinating world of equations together! Here are some practice questions designed to help you master the art of changing the subject of an equation. Each question is crafted to guide you step-by-step through the process of isolating different variables while applying algebraic principles.

Question 1:
You have a rectangular garden, and you know that the area (A) of the garden is given by the formula A = length × width. If the area of your garden is 50 square meters and the width is 5 meters, can you find the length of the garden?

Answer:
To find the length, we need to change the subject of the equation to length. The original equation is:

A = length × width

Rearranging this gives:

length = A / width

Now, substituting the values we have:

length = 50 / 5
length = 10 meters

So, the length of your garden is 10 meters.

Question 2:
Imagine you're trying to save money for a new bicycle. You know that your savings (S) can be calculated by the equation S = I - E, where I is your income and E is your expenses. If your income is 3000 rupees and your expenses are 1500 rupees, how much are you saving?

Answer:
To find savings, we will use the given equation. First, we can substitute the known values into the equation:

S = I - E
S = 3000 - 1500
S = 1500 rupees

You are saving 1500 rupees!

Question 3:
You are studying physics and learn that the formula for kinetic energy (KE) is given by KE = 0.5 × mass (m) × velocity (v)². If you want to find the velocity, how would you rearrange the formula?

Answer:
To isolate velocity, we need to change the subject of the equation. Starting with the formula:

KE = 0.5 × m × v²

First, we can multiply both sides by 2 to eliminate the 0.5:

2 × KE = m × v²

Next, divide both sides by mass (m):

(2 × KE) / m = v²

Now, take the square root of both sides to solve for velocity:

v = √((2 × KE) / m)

Now, you can calculate the velocity if you know the kinetic energy and mass!

Question 4:
In a science experiment, you are measuring the pressure (P) of a gas, which can be represented by the equation P = nRT/V, where n is the number of moles, R is the gas constant, T is the temperature, and V is the volume. How can you rearrange the formula to find volume (V)?

Answer:
To isolate volume, we start with the equation:

P = nRT/V

We can multiply both sides by V:

P × V = nRT

Now, divide both sides by P:

V = nRT/P

Now you have a formula to find the volume if you know the pressure, the number of moles, the gas constant, and the temperature!

Question 5:
You're helping a friend with a homework problem related to speed (s). The formula is given by s = d/t, where d is distance and t is time. If you want to find time (t), how would you rearrange the formula?

Answer:
Starting from the formula:

s = d/t

We can multiply both sides by time (t) to get rid of the fraction:

s × t = d

Next, divide both sides by speed (s):

t = d/s

Now you can calculate time if you know the distance and the speed!

These questions are designed to build your confidence in manipulating equations and understanding how to change the subject of a formula. Remember, practice makes perfect! Keep exploring different equations and scenarios, and you will become a master at equation manipulation. Happy learning!