Nari Says, The Sum Of 10 And One-third Of A Number Is 25. She Uses The Bar Model To Write An Equation To Represent Her Statement.${ \begin{tabular}{|c|c|} \hline 25 & \ \hline 10 & 1 3 N \frac{1}{3} N 3 1 ​ N \ \hline \end{tabular} }$Which

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Introduction

Linear equations are a fundamental concept in mathematics, and they play a crucial role in various fields such as physics, engineering, and economics. In this article, we will focus on solving linear equations, with a specific example from Nari's statement. We will use the bar model to represent the equation and then solve for the unknown variable.

Understanding the Bar Model

The bar model is a visual representation of an equation, where the bars are used to separate the different parts of the equation. In the given example, the bar model is used to represent the equation:

25

10 + (1/3)n

Breaking Down the Equation

Let's break down the equation and understand what each part represents:

  • 25: This is the total sum of the equation.
  • 10: This is a constant value that is added to the unknown variable.
  • (1/3)n: This represents one-third of the unknown variable.

Writing the Equation

Using the bar model, Nari writes the equation as:

25 = 10 + (1/3)n

Solving for the Unknown Variable

To solve for the unknown variable, we need to isolate the variable on one side of the equation. We can do this by subtracting 10 from both sides of the equation:

25 - 10 = (1/3)n

This simplifies to:

15 = (1/3)n

Multiplying Both Sides by 3

To get rid of the fraction, we can multiply both sides of the equation by 3:

3(15) = 3((1/3)n)

This simplifies to:

45 = n

Conclusion

In this article, we used the bar model to represent a linear equation and then solved for the unknown variable. We broke down the equation, wrote it in a mathematical form, and then solved for the variable by isolating it on one side of the equation. This is a simple example of solving linear equations, and there are many more complex equations that can be solved using similar techniques.

Real-World Applications

Linear equations have many real-world applications, such as:

  • Physics: Linear equations are used to describe the motion of objects, including the position, velocity, and acceleration of an object.
  • Engineering: Linear equations are used to design and optimize systems, such as electrical circuits and mechanical systems.
  • Economics: Linear equations are used to model economic systems, including the supply and demand of goods and services.

Tips and Tricks

Here are some tips and tricks for solving linear equations:

  • Use the bar model to visualize the equation and make it easier to understand.
  • Break down the equation into smaller parts and solve each part separately.
  • Use algebraic manipulations, such as adding or subtracting the same value to both sides of the equation, to isolate the variable.
  • Check your solution by plugging it back into the original equation.

Common Mistakes

Here are some common mistakes to avoid when solving linear equations:

  • Not using the bar model to visualize the equation.
  • Not breaking down the equation into smaller parts.
  • Not using algebraic manipulations to isolate the variable.
  • Not checking the solution by plugging it back into the original equation.

Conclusion

Introduction

In our previous article, we discussed how to solve linear equations using the bar model. In this article, we will provide a Q&A guide to help you understand and apply the concepts of solving linear equations.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable is 1. It can be written in the form ax + b = c, where a, b, and c are constants, and x is the variable.

Q: What is the bar model?

A: The bar model is a visual representation of an equation, where the bars are used to separate the different parts of the equation. It is a useful tool for solving linear equations.

Q: How do I use the bar model to solve a linear equation?

A: To use the bar model to solve a linear equation, follow these steps:

  1. Write the equation in a mathematical form.
  2. Use the bar model to visualize the equation.
  3. Break down the equation into smaller parts.
  4. Use algebraic manipulations to isolate the variable.
  5. Check your solution by plugging it back into the original equation.

Q: What are some common types of linear equations?

A: Some common types of linear equations include:

  • Simple linear equations: ax + b = c
  • Linear equations with fractions: ax + (b/c) = d
  • Linear equations with decimals: ax + (b.0) = c
  • Linear equations with variables on both sides: ax + by = c

Q: How do I solve a linear equation with fractions?

A: To solve a linear equation with fractions, follow these steps:

  1. Multiply both sides of the equation by the least common multiple (LCM) of the denominators.
  2. Simplify the equation.
  3. Use algebraic manipulations to isolate the variable.
  4. Check your solution by plugging it back into the original equation.

Q: How do I solve a linear equation with decimals?

A: To solve a linear equation with decimals, follow these steps:

  1. Multiply both sides of the equation by 10 to eliminate the decimal.
  2. Simplify the equation.
  3. Use algebraic manipulations to isolate the variable.
  4. Check your solution by plugging it back into the original equation.

Q: How do I solve a linear equation with variables on both sides?

A: To solve a linear equation with variables on both sides, follow these steps:

  1. Add or subtract the same value to both sides of the equation to eliminate one of the variables.
  2. Use algebraic manipulations to isolate the variable.
  3. Check your solution by plugging it back into the original equation.

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

A: Some common mistakes to avoid when solving linear equations include:

  • Not using the bar model to visualize the equation.
  • Not breaking down the equation into smaller parts.
  • Not using algebraic manipulations to isolate the variable.
  • Not checking the solution by plugging it back into the original equation.

Q: How can I practice solving linear equations?

A: You can practice solving linear equations by:

  • Working through example problems.
  • Using online resources, such as math websites and apps.
  • Creating your own practice problems.
  • Joining a study group or working with a tutor.

Conclusion

In conclusion, solving linear equations is a crucial skill in mathematics, and it has many real-world applications. By using the bar model, breaking down the equation, and using algebraic manipulations, we can solve linear equations and understand the underlying concepts. Remember to use the tips and tricks provided in this article to avoid common mistakes and become proficient in solving linear equations.