Practice: Write And Solve The Equation 2 5 \frac{2}{5} 5 2 ​ Of A Number Is 16. What Is The Number?First, Write An Equation To Describe The Situation: 2 5 M = 16 \frac{2}{5} M = 16 5 2 ​ M = 16 What Is The Number?The Number Is □ \square □

Introduction

In mathematics, equations are a fundamental concept that helps us solve problems and understand relationships between variables. In this article, we will focus on solving a specific type of equation, where a fraction of a number is equal to a given value. We will use the example of $\frac{2}{5}$ of a number is 16 to illustrate the steps involved in solving such equations.

Understanding the Problem

The problem states that $\frac{2}{5}$ of a number is 16. This means that if we multiply the number by $\frac{2}{5}$, we should get 16 as the result. We can represent this situation using an equation:

$\frac{2}{5} m = 16$

where $m$ is the unknown number.

Writing the Equation

To write the equation, we need to identify the unknown quantity and the given information. In this case, the unknown quantity is the number, represented by $m$. The given information is that $\frac{2}{5}$ of the number is 16.

We can write the equation by multiplying the number by $\frac{2}{5}$ and setting it equal to 16:

$\frac{2}{5} m = 16$

Solving the Equation

To solve the equation, we need to isolate the unknown quantity, $m$. We can do this by multiplying both sides of the equation by the reciprocal of $\frac{2}{5}$, which is $\frac{5}{2}$.

$\frac{5}{2} \times \frac{2}{5} m = \frac{5}{2} \times 16$

Simplifying the left-hand side of the equation, we get:

$m = \frac{5}{2} \times 16$

Now, we can simplify the right-hand side of the equation by multiplying $\frac{5}{2}$ by 16:

$m = 40$

Conclusion

In this article, we have solved an equation where $\frac{2}{5}$ of a number is 16. We have shown that the number is 40. This problem illustrates the importance of understanding fractions and how to use them to solve equations.

Tips and Tricks

• When solving equations, make sure to identify the unknown quantity and the given information.
• Use the reciprocal of a fraction to isolate the unknown quantity.
• Simplify the equation by multiplying both sides by the reciprocal of the fraction.

Practice Problems

1. $\frac{3}{4}$ of a number is 24. What is the number?
2. $\frac{2}{3}$ of a number is 18. What is the number?
3. $\frac{1}{2}$ of a number is 12. What is the number?

Answer Key

1. 32
2. 27
3. 24

Discussion

This problem is a great example of how to use fractions to solve equations. The key is to identify the unknown quantity and the given information, and then use the reciprocal of the fraction to isolate the unknown quantity. We can use this technique to solve a wide range of problems involving fractions and equations.

Related Topics

• Fractions: Understanding and working with fractions is essential for solving equations involving fractions.
• Equations: Solving equations is a fundamental concept in mathematics, and understanding how to solve equations is crucial for solving problems involving fractions.
• Algebra: Algebra is a branch of mathematics that deals with solving equations and manipulating variables. Understanding algebra is essential for solving problems involving fractions and equations.

Conclusion

Introduction

In our previous article, we discussed how to solve equations involving fractions. We provided a step-by-step guide on how to write and solve the equation $\frac{2}{5}$ of a number is 16. In this article, we will provide a Q&A guide to help you better understand how to solve equations involving fractions.

Q: What is the first step in solving an equation involving a fraction?

A: The first step in solving an equation involving a fraction is to identify the unknown quantity and the given information. You need to understand what the problem is asking and what information is provided.

Q: How do I write an equation to describe the situation?

A: To write an equation, you need to represent the unknown quantity as a variable (usually represented by a letter such as $m$) and the given information as a numerical value. For example, if the problem states that $\frac{2}{5}$ of a number is 16, you can write the equation as $\frac{2}{5} m = 16$.

Q: How do I solve an equation involving a fraction?

A: To solve an equation involving a fraction, you need to isolate the unknown quantity by multiplying both sides of the equation by the reciprocal of the fraction. For example, if the equation is $\frac{2}{5} m = 16$, you can multiply both sides by $\frac{5}{2}$ to get $m = \frac{5}{2} \times 16$.

Q: What is the reciprocal of a fraction?

A: The reciprocal of a fraction is obtained by swapping the numerator and the denominator. For example, the reciprocal of $\frac{2}{5}$ is $\frac{5}{2}$.

Q: How do I simplify an equation involving a fraction?

A: To simplify an equation involving a fraction, you need to multiply both sides of the equation by the reciprocal of the fraction. This will eliminate the fraction and leave you with a simple equation.

Q: What are some common mistakes to avoid when solving equations involving fractions?

A: Some common mistakes to avoid when solving equations involving fractions include:

• Not identifying the unknown quantity and the given information
• Not using the reciprocal of the fraction to isolate the unknown quantity
• Not simplifying the equation
• Not checking the solution to ensure it is correct

Q: How can I practice solving equations involving fractions?

A: You can practice solving equations involving fractions by working through examples and exercises. You can also try solving problems involving fractions in your daily life, such as calculating tips or discounts.

Q: What are some real-world applications of solving equations involving fractions?

A: Solving equations involving fractions has many real-world applications, including:

• Calculating tips and discounts
• Determining the cost of materials for a project
• Calculating the area and perimeter of a shape
• Determining the amount of time it will take to complete a task

Conclusion

In conclusion, solving equations involving fractions is a crucial skill in mathematics. By understanding how to use fractions to solve equations, you can solve a wide range of problems and develop a deeper understanding of mathematical concepts. We hope this Q&A guide has provided a clear and concise overview of how to solve equations involving fractions.

Practice Problems

1. $\frac{3}{4}$ of a number is 24. What is the number?
2. $\frac{2}{3}$ of a number is 18. What is the number?
3. $\frac{1}{2}$ of a number is 12. What is the number?

Answer Key

1. 32
2. 27
3. 24

Discussion

This Q&A guide is designed to help you better understand how to solve equations involving fractions. By working through the examples and exercises, you can develop a deeper understanding of mathematical concepts and improve your problem-solving skills. We hope this guide has been helpful in your journey to mastering equations involving fractions.