Make $p$ The Subject Of The Formula: $m = 5n + 2p$
Introduction
In algebra, it is often necessary to isolate a variable and make it the subject of a formula. This involves rearranging the formula to express the variable in terms of other variables. In this article, we will explore how to make p the subject of the formula m = 5n + 2p.
Understanding the Formula
The given formula is m = 5n + 2p. This formula states that the value of m is equal to 5 times the value of n, plus 2 times the value of p. To make p the subject of the formula, we need to isolate p and express it in terms of m and n.
Step 1: Subtract 5n from Both Sides
To isolate p, we need to get rid of the term 5n on the right-hand side of the formula. We can do this by subtracting 5n from both sides of the equation.
m = 5n + 2p
Subtracting 5n from both sides gives us:
m - 5n = 2p
Step 2: Divide Both Sides by 2
Now that we have 2p on the right-hand side, we need to get rid of the coefficient 2. We can do this by dividing both sides of the equation by 2.
(m - 5n) / 2 = p
Step 3: Simplify the Left-Hand Side
The left-hand side of the equation can be simplified by combining the terms inside the parentheses.
(m - 5n) / 2 = p
This can be rewritten as:
(m - 5n) / 2 = p
The Final Formula
After simplifying the left-hand side, we are left with the final formula:
p = (m - 5n) / 2
This formula expresses p in terms of m and n, making p the subject of the original formula.
Example
Let's use an example to illustrate how to use the final formula. Suppose we are given the values of m and n, and we want to find the value of p.
m = 10 n = 2
Substituting these values into the final formula, we get:
p = (10 - 5(2)) / 2
p = (10 - 10) / 2
p = 0 / 2
p = 0
Therefore, the value of p is 0.
Conclusion
In this article, we have shown how to make p the subject of the formula m = 5n + 2p. We have used a step-by-step approach to isolate p and express it in terms of m and n. The final formula is p = (m - 5n) / 2, which can be used to find the value of p given the values of m and n.
Tips and Variations
- To make p the subject of the formula, we need to isolate p and express it in terms of m and n.
- We can use the same steps to make p the subject of other formulas, such as m = 3p + 2n.
- To make p the subject of a formula with multiple terms, we need to use the distributive property to expand the terms and then isolate p.
Common Mistakes
- Not isolating p completely, leaving other terms on the right-hand side.
- Not using the correct order of operations, such as not evaluating expressions inside parentheses first.
- Not checking the final formula for errors, such as not simplifying the left-hand side.
Real-World Applications
- Making p the subject of a formula can be used in a variety of real-world applications, such as:
- Physics: to calculate the momentum of an object given its mass and velocity.
- Engineering: to design a system that meets specific requirements, such as a bridge that can support a certain amount of weight.
- Economics: to model the behavior of a market given certain variables, such as supply and demand.
Make p the Subject of the Formula: m = 5n + 2p - Q&A =====================================================
Introduction
In our previous article, we explored how to make p the subject of the formula m = 5n + 2p. In this article, we will answer some common questions related to making p the subject of a formula.
Q: What is the purpose of making p the subject of a formula?
A: The purpose of making p the subject of a formula is to isolate p and express it in terms of other variables, such as m and n. This allows us to find the value of p given the values of m and n.
Q: How do I know when to make p the subject of a formula?
A: You should make p the subject of a formula when you need to find the value of p given the values of m and n. This is often the case in algebraic equations and formulas.
Q: What are the steps to make p the subject of a formula?
A: The steps to make p the subject of a formula are:
- Subtract 5n from both sides of the equation.
- Divide both sides of the equation by 2.
- Simplify the left-hand side of the equation.
Q: What if the formula has multiple terms?
A: If the formula has multiple terms, you will need to use the distributive property to expand the terms and then isolate p.
Q: What if the formula has a coefficient other than 2?
A: If the formula has a coefficient other than 2, you will need to divide both sides of the equation by the coefficient to isolate p.
Q: Can I make p the subject of a formula with a negative coefficient?
A: Yes, you can make p the subject of a formula with a negative coefficient. Simply follow the same steps as before, and the negative sign will be carried through to the final formula.
Q: What if I get stuck or make a mistake?
A: If you get stuck or make a mistake, don't worry! Simply re-read the steps and try again. You can also ask a teacher or tutor for help.
Q: Are there any real-world applications of making p the subject of a formula?
A: Yes, there are many real-world applications of making p the subject of a formula. Some examples include:
- Physics: to calculate the momentum of an object given its mass and velocity.
- Engineering: to design a system that meets specific requirements, such as a bridge that can support a certain amount of weight.
- Economics: to model the behavior of a market given certain variables, such as supply and demand.
Q: Can I use making p the subject of a formula to solve other types of equations?
A: Yes, you can use making p the subject of a formula to solve other types of equations, such as quadratic equations and systems of equations.
Conclusion
In this article, we have answered some common questions related to making p the subject of a formula. We have also provided examples and real-world applications to illustrate the importance of making p the subject of a formula.
Tips and Variations
- To make p the subject of a formula, you need to isolate p and express it in terms of other variables.
- You can use the same steps to make p the subject of other formulas, such as m = 3p + 2n.
- To make p the subject of a formula with multiple terms, you need to use the distributive property to expand the terms and then isolate p.
Common Mistakes
- Not isolating p completely, leaving other terms on the right-hand side.
- Not using the correct order of operations, such as not evaluating expressions inside parentheses first.
- Not checking the final formula for errors, such as not simplifying the left-hand side.
Real-World Applications
- Making p the subject of a formula can be used in a variety of real-world applications, such as:
- Physics: to calculate the momentum of an object given its mass and velocity.
- Engineering: to design a system that meets specific requirements, such as a bridge that can support a certain amount of weight.
- Economics: to model the behavior of a market given certain variables, such as supply and demand.