Stan Ran $4 \frac{7}{10}$ Miles, Which Was $1 \frac{3}{10}$ Fewer Miles Than Matt Ran. Four Students Wrote And Solved Equations To Find $m$, The Number Of Miles That Matt Ran. Which Student Wrote And Solved The Equation

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Introduction

In mathematics, solving equations is a crucial skill that helps us understand and describe real-world problems. In this case, we are given that Stan ran $4 \frac{7}{10}$ miles, which was $1 \frac{3}{10}$ fewer miles than Matt ran. Four students were tasked with writing and solving equations to find the number of miles that Matt ran. In this article, we will explore the different approaches that these students might have taken to solve this problem.

Understanding the Problem

Let's start by understanding the problem. We are given that Stan ran $4 \frac{7}{10}$ miles, and Matt ran $1 \frac{3}{10}$ more miles than Stan. To find the number of miles that Matt ran, we need to add the distance that Stan ran to the additional distance that Matt ran.

Writing the Equation

One way to approach this problem is to write an equation that represents the situation. Let's use the variable $m$ to represent the number of miles that Matt ran. We can write the equation as:

$$m = 4 \frac{7}{10} + 1 \frac{3}{10}$$

Simplifying the Equation

To simplify the equation, we can convert the mixed numbers to improper fractions. We can do this by multiplying the whole number part by the denominator and then adding the numerator.

$$m = \frac{47}{10} + \frac{13}{10}$$

Combining Like Terms

Now that we have the equation in terms of improper fractions, we can combine like terms by adding the numerators.

$$m = \frac{47 + 13}{10}$$

Simplifying the Fraction

To simplify the fraction, we can divide the numerator by the denominator.

$$m = \frac{60}{10}$$

Reducing the Fraction

Finally, we can reduce the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 10.

$$m = 6$$

Conclusion

In this article, we explored the different approaches that students might take to solve the problem of finding the number of miles that Matt ran. We wrote an equation that represented the situation, simplified the equation by converting mixed numbers to improper fractions, combined like terms, simplified the fraction, and reduced the fraction to find the final answer. By following these steps, we can confidently say that Matt ran 6 miles.

Alternative Approaches

Another way to approach this problem is to use algebraic thinking. We can let $m$ represent the number of miles that Matt ran and write an equation that represents the situation.

$$m = 4 \frac{7}{10} + 1 \frac{3}{10}$$

We can then simplify the equation by converting the mixed numbers to improper fractions.

$$m = \frac{47}{10} + \frac{13}{10}$$

We can combine like terms by adding the numerators.

$$m = \frac{47 + 13}{10}$$

We can simplify the fraction by dividing the numerator by the denominator.

$$m = \frac{60}{10}$$

We can reduce the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 10.

$$m = 6$$

Using a Number Line

Another way to approach this problem is to use a number line. We can start at the point that represents the number of miles that Stan ran, which is $4 \frac{7}{10}$. We can then move $1 \frac{3}{10}$ units to the right to find the point that represents the number of miles that Matt ran.

Conclusion

In this article, we explored the different approaches that students might take to solve the problem of finding the number of miles that Matt ran. We wrote an equation that represented the situation, simplified the equation by converting mixed numbers to improper fractions, combined like terms, simplified the fraction, and reduced the fraction to find the final answer. We also used algebraic thinking and a number line to approach the problem. By following these steps, we can confidently say that Matt ran 6 miles.

Real-World Applications

This problem has real-world applications in many areas, such as sports, transportation, and construction. For example, in sports, a coach might need to calculate the distance that a player ran in a game. In transportation, a driver might need to calculate the distance that they traveled to get to a destination. In construction, a builder might need to calculate the distance that they need to travel to get to a specific location.

Conclusion

In conclusion, solving equations is a crucial skill that helps us understand and describe real-world problems. In this article, we explored the different approaches that students might take to solve the problem of finding the number of miles that Matt ran. We wrote an equation that represented the situation, simplified the equation by converting mixed numbers to improper fractions, combined like terms, simplified the fraction, and reduced the fraction to find the final answer. We also used algebraic thinking and a number line to approach the problem. By following these steps, we can confidently say that Matt ran 6 miles.

Final Answer

The final answer is 6.

Introduction

In our previous article, we explored the different approaches that students might take to solve the problem of finding the number of miles that Matt ran. In this article, we will answer some frequently asked questions about solving equations.

Q: What is an equation?

A: An equation is a statement that says two things are equal. It is a mathematical statement that contains an equals sign (=) and can be used to solve for a variable.

Q: What is a variable?

A: A variable is a letter or symbol that represents a value that can change. In the equation $m = 4 \frac{7}{10} + 1 \frac{3}{10}$, the variable $m$ represents the number of miles that Matt ran.

Q: How do I simplify an equation?

A: To simplify an equation, you can combine like terms by adding or subtracting the coefficients of the same variable. You can also convert mixed numbers to improper fractions and simplify the fraction.

Q: What is a like term?

A: A like term is a term that has the same variable and coefficient. For example, in the equation $m = 4 \frac{7}{10} + 1 \frac{3}{10}$, the terms $4 \frac{7}{10}$ and $1 \frac{3}{10}$ are like terms because they both have the variable $m$.

Q: How do I solve an equation?

A: To solve an equation, you can use algebraic thinking and manipulate the equation to isolate the variable. You can add or subtract the same value to both sides of the equation, multiply or divide both sides of the equation by the same value, or use inverse operations to solve for the variable.

Q: What is an inverse operation?

A: An inverse operation is an operation that undoes another operation. For example, if you add 2 to a number, the inverse operation is to subtract 2 from the number.

Q: How do I use a number line to solve an equation?

A: To use a number line to solve an equation, you can start at the point that represents the value of the variable and move the correct number of units to the right or left to find the solution.

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

A: Solving equations has many real-world applications in areas such as sports, transportation, and construction. For example, a coach might need to calculate the distance that a player ran in a game, a driver might need to calculate the distance that they traveled to get to a destination, or a builder might need to calculate the distance that they need to travel to get to a specific location.

Q: Why is it important to solve equations?

A: Solving equations is an important skill that helps us understand and describe real-world problems. It is a crucial part of mathematics and is used in many areas of life.

Q: Can you give an example of a real-world problem that involves solving an equation?

A: Yes, here is an example of a real-world problem that involves solving an equation:

A car travels from City A to City B at an average speed of 60 miles per hour. If the distance between the two cities is 240 miles, how many hours will it take to travel from City A to City B?

To solve this problem, we can use the equation:

Time = Distance / Speed

We can plug in the values and solve for time:

Time = 240 miles / 60 miles per hour

Time = 4 hours

Therefore, it will take 4 hours to travel from City A to City B.

Conclusion

In this article, we answered some frequently asked questions about solving equations. We discussed what an equation is, what a variable is, how to simplify an equation, and how to solve an equation. We also discussed some real-world applications of solving equations and why it is an important skill. By following these steps, we can confidently say that solving equations is a crucial part of mathematics and is used in many areas of life.

Final Answer

The final answer is 4.