How to Solve for x in a Proportion

Oct 13, 2025 by magicalceylontours.com 116 views

Understanding Proportions and Solving for x

In mathematics, proportions are used to compare two ratios or fractions. A proportion is a statement that two ratios are equal, and it is often written in the form of an equation. In this article, we will explore how to solve for x in a proportion, using the given equation $\frac{3}{x} = \frac{15}{40}$ .

What is a Proportion?

A proportion is a statement that two ratios are equal. It is often written in the form of an equation, where the two ratios are set equal to each other. For example, the proportion $\frac{3}{x} = \frac{15}{40}$ states that the ratio of 3 to x is equal to the ratio of 15 to 40.

How to Solve for x in a Proportion

To solve for x in a proportion, we need to follow these steps:

Cross-multiply: Multiply the numerator of the first ratio by the denominator of the second ratio, and multiply the numerator of the second ratio by the denominator of the first ratio.
Simplify: Simplify the resulting equation by dividing both sides by the common factor.
Solve for x: Solve for x by isolating it on one side of the equation.

Solving the Given Proportion

Let's apply these steps to the given proportion $\frac{3}{x} = \frac{15}{40}$ .

Step 1: Cross-multiply

To cross-multiply, we multiply the numerator of the first ratio (3) by the denominator of the second ratio (40), and multiply the numerator of the second ratio (15) by the denominator of the first ratio (x).

$\begin{aligned} 3 \times 40 &= 15 \times x \\ 120 &= 15x \end{aligned}$

Step 2: Simplify

To simplify the equation, we divide both sides by the common factor (15).

$\begin{aligned} \frac{120}{15} &= \frac{15x}{15} \\ 8 &= x \end{aligned}$

Step 3: Solve for x

We have now solved for x, and the value of x is 8.

Conclusion

In this article, we have explored how to solve for x in a proportion, using the given equation $\frac{3}{x} = \frac{15}{40}$ . We have followed the steps of cross-multiplying, simplifying, and solving for x. The value of x is 8.

Answer

The correct answer is B. 8.

Additional Examples

Here are some additional examples of proportions and how to solve for x:

$\frac{2}{x} = \frac{10}{20}$ : Solve for x.
$\frac{5}{x} = \frac{25}{50}$ : Solve for x.
$\frac{3}{x} = \frac{12}{40}$ : Solve for x.

Practice Problems

Try solving the following proportions:

$\frac{4}{x} = \frac{20}{50}$
$\frac{6}{x} = \frac{30}{60}$
$\frac{9}{x} = \frac{45}{90}$

Solutions

Here are the solutions to the practice problems:

$\frac{4}{x} = \frac{20}{50}$ : Solve for x.
$\frac{6}{x} = \frac{30}{60}$ : Solve for x.
$\frac{9}{x} = \frac{45}{90}$ : Solve for x.

Answer Key

Here is the answer key for the practice problems:

$\frac{4}{x} = \frac{20}{50}$ : x = 5
$\frac{6}{x} = \frac{30}{60}$ : x = 10
$\frac{9}{x} = \frac{45}{90}$ : x = 10
Frequently Asked Questions (FAQs) About Proportions and Solving for x =====================================================================

Understanding Proportions and Solving for x

In our previous article, we explored how to solve for x in a proportion, using the given equation $\frac{3}{x} = \frac{15}{40}$ . In this article, we will answer some frequently asked questions (FAQs) about proportions and solving for x.

Q: What is a proportion?

A: A proportion is a statement that two ratios are equal. It is often written in the form of an equation, where the two ratios are set equal to each other.

Q: How do I know if a proportion is true or false?

A: To determine if a proportion is true or false, you can cross-multiply and simplify the equation. If the resulting equation is true, then the proportion is true. If the resulting equation is false, then the proportion is false.

Q: What is cross-multiplication?

A: Cross-multiplication is a technique used to solve proportions. It involves multiplying the numerator of the first ratio by the denominator of the second ratio, and multiplying the numerator of the second ratio by the denominator of the first ratio.

Q: How do I simplify a proportion?

A: To simplify a proportion, you can divide both sides of the equation by the common factor.

Q: What is the common factor?

A: The common factor is the number that is common to both sides of the equation.

Q: How do I solve for x in a proportion?

A: To solve for x in a proportion, you can follow these steps:

Cross-multiply
Simplify
Solve for x

Q: What if I have a proportion with fractions?

A: If you have a proportion with fractions, you can simplify the fractions before solving for x.

Q: Can I use proportions to solve equations with variables?

A: Yes, you can use proportions to solve equations with variables. However, you need to make sure that the proportion is true before solving for the variable.

Q: How do I know if a proportion is an identity or not?

A: A proportion is an identity if it is true for all values of x. If a proportion is not an identity, then it is not true for all values of x.

Q: Can I use proportions to solve inequalities?

A: Yes, you can use proportions to solve inequalities. However, you need to make sure that the proportion is true before solving for the variable.

Q: What are some common mistakes to avoid when solving proportions?

A: Some common mistakes to avoid when solving proportions include:

Not cross-multiplying
Not simplifying the equation
Not solving for x
Not checking if the proportion is an identity or not