Writing an Equation to Describe the Situation

Oct 13, 2025 by miodeya.com 63 views

Introduction

In mathematics, solving equations is a fundamental concept that helps us find the value of unknown variables. In this article, we will explore how to solve an equation that involves a fraction and a variable. We will use a step-by-step approach to isolate the variable and find its value.

Writing an Equation to Describe the Situation

The problem states that the difference of a number and $\frac{4}{3}$ is $\frac{11}{3}$ . To write an equation that describes this situation, we can use the following format:

$y - \text{something} = \text{result}$

In this case, the "something" is $\frac{4}{3}$ , and the "result" is $\frac{11}{3}$ . Therefore, the equation that describes the situation is:

$y - \frac{4}{3} = \frac{11}{3}$

Solving the Equation

To solve the equation, we need to isolate the variable $y$ . We can do this by adding $\frac{4}{3}$ to both sides of the equation. This will cancel out the $\frac{4}{3}$ on the left-hand side, leaving us with just $y$ .

$y - \frac{4}{3} + \frac{4}{3} = \frac{11}{3} + \frac{4}{3}$

Simplifying the left-hand side, we get:

$y = \frac{11}{3} + \frac{4}{3}$

Adding Fractions

To add fractions, we need to have the same denominator. In this case, the denominators are both $3$ , so we can add the fractions directly.

$\frac{11}{3} + \frac{4}{3} = \frac{15}{3}$

Simplifying the Fraction

The fraction $\frac{15}{3}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is $3$ .

$\frac{15}{3} = \frac{15 \div 3}{3 \div 3} = \frac{5}{1}$

The Final Answer

Therefore, the number is $\boxed{5}$ .

Conclusion

In this article, we solved an equation that involved a fraction and a variable. We used a step-by-step approach to isolate the variable and find its value. The final answer is $\boxed{5}$ .

Frequently Asked Questions

What is the difference of a number and $\frac{4}{3}$ ?
How do you solve an equation that involves a fraction and a variable?
What is the value of the number in the equation $y - \frac{4}{3} = \frac{11}{3}$ ?

Step-by-Step Solution

Write an equation to describe the situation: $y - \frac{4}{3} = \frac{11}{3}$
Add $\frac{4}{3}$ to both sides of the equation to isolate the variable $y$ .
Simplify the left-hand side of the equation.
Add the fractions on the right-hand side of the equation.
Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor.
The final answer is $\boxed{5}$ .

References

[1] "Algebra" by Michael Artin
[2] "Elementary and Intermediate Algebra" by Marvin L. Bittinger
[3] "College Algebra" by James Stewart

Introduction

In our previous article, we solved an equation that involved a fraction and a variable. We used a step-by-step approach to isolate the variable and find its value. In this article, we will answer some frequently asked questions related to the problem.

Q&A

Q: What is the difference of a number and $\frac{4}{3}$ ?

A: The difference of a number and $\frac{4}{3}$ is the result of subtracting $\frac{4}{3}$ from the number. In other words, if we have a number $y$ , the difference of $y$ and $\frac{4}{3}$ is $y - \frac{4}{3}$ .

Q: How do you solve an equation that involves a fraction and a variable?

A: To solve an equation that involves a fraction and a variable, we need to isolate the variable. We can do this by adding or subtracting the same value to both sides of the equation. In the case of the equation $y - \frac{4}{3} = \frac{11}{3}$ , we can add $\frac{4}{3}$ to both sides to isolate the variable $y$ .

Q: What is the value of the number in the equation $y - \frac{4}{3} = \frac{11}{3}$ ?

A: To find the value of the number in the equation $y - \frac{4}{3} = \frac{11}{3}$ , we need to isolate the variable $y$ . We can do this by adding $\frac{4}{3}$ to both sides of the equation. This will give us $y = \frac{11}{3} + \frac{4}{3}$ . Simplifying the right-hand side, we get $y = \frac{15}{3}$ . Finally, we can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is $3$ . This gives us $y = \frac{5}{1}$ , or simply $y = 5$ .

Q: Can you explain the concept of adding fractions?

A: Yes, certainly. Adding fractions involves combining two or more fractions with the same denominator. To add fractions, we need to have the same denominator. In the case of the equation $y - \frac{4}{3} = \frac{11}{3}$ , we have two fractions with the same denominator, which is $3$ . We can add these fractions directly by adding the numerators and keeping the denominator the same. In this case, we get $\frac{11}{3} + \frac{4}{3} = \frac{15}{3}$ .

Q: Can you explain the concept of simplifying fractions?

A: Yes, certainly. Simplifying fractions involves reducing a fraction to its simplest form by dividing both the numerator and the denominator by their greatest common divisor. In the case of the fraction $\frac{15}{3}$ , we can simplify it by dividing both the numerator and the denominator by their greatest common divisor, which is $3$ . This gives us $\frac{15 \div 3}{3 \div 3} = \frac{5}{1}$ .

Q: What is the final answer to the equation $y - \frac{4}{3} = \frac{11}{3}$ ?

A: The final answer to the equation $y - \frac{4}{3} = \frac{11}{3}$ is $y = 5$ .

Conclusion

In this article, we answered some frequently asked questions related to the problem of finding the difference of a number and $\frac{4}{3}$ , which is $\frac{11}{3}$ . We explained the concepts of adding fractions and simplifying fractions, and we provided step-by-step solutions to the equation $y - \frac{4}{3} = \frac{11}{3}$ .

References

[1] "Algebra" by Michael Artin
[2] "Elementary and Intermediate Algebra" by Marvin L. Bittinger
[3] "College Algebra" by James Stewart