Finding the Number to Be Added

Oct 13, 2025 by windailys.com 24 views

Introduction

In mathematics, fractions are a fundamental concept that represents a part of a whole. When dealing with fractions, we often encounter problems that require us to find the difference between two fractions or add a certain number to a fraction to obtain another fraction. In this article, we will explore the problem of finding the number that needs to be added to $$\frac{7}{12}$$ to get $$\frac{4}{15}$$.

Understanding the Problem

To solve this problem, we need to find the common denominator of the two fractions, which is the least common multiple (LCM) of 12 and 15. The LCM of 12 and 15 is 60. We can rewrite both fractions with the common denominator of 60.

\frac{7}{12} = \frac{7 \times 5}{12 \times 5} = \frac{35}{60}

\frac{4}{15} = \frac{4 \times 4}{15 \times 4} = \frac{16}{60}

Finding the Number to Be Added

Now that we have both fractions with the common denominator of 60, we can find the number that needs to be added to $$\frac{35}{60}$$ to get $$\frac{16}{60}$$. To do this, we need to subtract the numerator of the first fraction from the numerator of the second fraction.

\frac{16}{60} - \frac{35}{60} = \frac{16 - 35}{60} = \frac{-19}{60}

Conclusion

The number that needs to be added to $$\frac{7}{12}$$ to get $$\frac{4}{15}$$ is $$\frac{-19}{60}$$. This means that if we add $$\frac{-19}{60}$$ to $$\frac{7}{12}$$, we will get $$\frac{4}{15}$$.

Real-World Applications

This problem may seem abstract, but it has real-world applications in various fields such as finance, engineering, and science. For example, in finance, we may need to calculate the interest rate on a loan or the return on investment (ROI) of a stock. In engineering, we may need to calculate the stress on a material or the strain on a structure. In science, we may need to calculate the concentration of a solution or the density of a substance.

Tips and Tricks

When dealing with fractions, it's essential to find the common denominator to add or subtract them. You can use the LCM of the denominators to find the common denominator. Additionally, when subtracting fractions, make sure to subtract the numerators while keeping the denominators the same.

Common Mistakes

One common mistake when dealing with fractions is to add or subtract the denominators instead of the numerators. This can lead to incorrect results. Another mistake is to forget to find the common denominator, which can also lead to incorrect results.

Final Thoughts

In conclusion, finding the number that needs to be added to $$\frac{7}{12}$$ to get $$\frac{4}{15}$$ requires us to find the common denominator of the two fractions and subtract the numerators while keeping the denominators the same. This problem may seem simple, but it has real-world applications in various fields. By following the tips and tricks outlined in this article, you can avoid common mistakes and arrive at the correct solution.

Additional Resources

For more information on fractions and how to add and subtract them, check out the following resources:

Khan Academy: Fractions
Mathway: Fractions
Wolfram Alpha: Fractions

Frequently Asked Questions

Q: What is the common denominator of 12 and 15? A: The common denominator of 12 and 15 is 60.

Q: How do I find the number that needs to be added to $$\frac{7}{12}$$ to get $$\frac{4}{15}$$? A: To find the number that needs to be added, subtract the numerator of the first fraction from the numerator of the second fraction while keeping the denominators the same.

Q: What is the number that needs to be added to $$\frac7}{12}$$ to get $$\frac{4}{15}$$? A The number that needs to be added is $$\frac{-19{60}$$.

Q&A Article

In this article, we will answer some of the most frequently asked questions related to the problem of finding the number that needs to be added to $$\frac{7}{12}$$ to get $$\frac{4}{15}$$.

Q: What is the common denominator of 12 and 15?

A: The common denominator of 12 and 15 is 60.

The common denominator is the least common multiple (LCM) of the two denominators. In this case, the LCM of 12 and 15 is 60.

Q: How do I find the number that needs to be added to $$\frac{7}{12}$$ to get $$\frac{4}{15}$$?

A: To find the number that needs to be added, subtract the numerator of the first fraction from the numerator of the second fraction while keeping the denominators the same.

This can be done by rewriting both fractions with the common denominator of 60, and then subtracting the numerators.

Q: What is the number that needs to be added to $$\frac{7}{12}$$ to get $$\frac{4}{15}$$?

A: The number that needs to be added is $$\frac{-19}{60}$$.

This is the result of subtracting the numerator of the first fraction from the numerator of the second fraction while keeping the denominators the same.

Q: Why do I need to find the common denominator?

A: You need to find the common denominator to add or subtract fractions. If you don't find the common denominator, you may get incorrect results.

Finding the common denominator ensures that you are comparing the same units, which is essential when working with fractions.

Q: Can I use a calculator to find the number that needs to be added?

A: Yes, you can use a calculator to find the number that needs to be added. However, it's essential to understand the concept behind the calculation.

Using a calculator can help you arrive at the correct answer quickly, but it's still important to understand the underlying math.

Q: What if I have a fraction with a negative numerator?

A: If you have a fraction with a negative numerator, you can still find the number that needs to be added. Simply subtract the numerator of the first fraction from the numerator of the second fraction while keeping the denominators the same.

The sign of the numerator does not affect the calculation.

Q: Can I use this method to find the number that needs to be added to any two fractions?

A: Yes, you can use this method to find the number that needs to be added to any two fractions. As long as you find the common denominator and subtract the numerators while keeping the denominators the same, you will arrive at the correct answer.

This method is applicable to any two fractions, regardless of their denominators.

Q: What if I have a fraction with a decimal numerator?

A: If you have a fraction with a decimal numerator, you can still find the number that needs to be added. Simply convert the decimal to a fraction and then proceed with the calculation.

Converting the decimal to a fraction will allow you to work with whole numbers, making the calculation easier.

Q: Can I use this method to find the number that needs to be added to a fraction and a whole number?

A: Yes, you can use this method to find the number that needs to be added to a fraction and a whole number. As long as you find the common denominator and subtract the numerators while keeping the denominators the same, you will arrive at the correct answer.

This method is applicable to any combination of fractions and whole numbers.

Q: What if I have a fraction with a negative denominator?

A: If you have a fraction with a negative denominator, you can still find the number that needs to be added. Simply rewrite the fraction with a positive denominator and then proceed with the calculation.

Rewriting the fraction with a positive denominator will allow you to work with whole numbers, making the calculation easier.

Q: Can I use this method to find the number that needs to be added to a fraction and a mixed number?

A: Yes, you can use this method to find the number that needs to be added to a fraction and a mixed number. As long as you find the common denominator and subtract the numerators while keeping the denominators the same, you will arrive at the correct answer.

This method is applicable to any combination of fractions and mixed numbers.

Q: What if I have a fraction with a variable numerator?

A: If you have a fraction with a variable numerator, you can still find the number that needs to be added. Simply substitute the variable with a value and then proceed with the calculation.

Substituting the variable with a value will allow you to work with whole numbers, making the calculation easier.

Q: Can I use this method to find the number that needs to be added to a fraction and a fraction with a variable denominator?

A: Yes, you can use this method to find the number that needs to be added to a fraction and a fraction with a variable denominator. As long as you find the common denominator and subtract the numerators while keeping the denominators the same, you will arrive at the correct answer.

This method is applicable to any combination of fractions and fractions with variable denominators.

Q: What if I have a fraction with a negative variable numerator?

A: If you have a fraction with a negative variable numerator, you can still find the number that needs to be added. Simply substitute the variable with a value and then proceed with the calculation.

Substituting the variable with a value will allow you to work with whole numbers, making the calculation easier.

Q: Can I use this method to find the number that needs to be added to a fraction and a fraction with a negative variable denominator?

A: Yes, you can use this method to find the number that needs to be added to a fraction and a fraction with a negative variable denominator. As long as you find the common denominator and subtract the numerators while keeping the denominators the same, you will arrive at the correct answer.

This method is applicable to any combination of fractions and fractions with negative variable denominators.

Q: What if I have a fraction with a variable denominator and a variable numerator?

A: If you have a fraction with a variable denominator and a variable numerator, you can still find the number that needs to be added. Simply substitute the variables with values and then proceed with the calculation.

Substituting the variables with values will allow you to work with whole numbers, making the calculation easier.

Q: Can I use this method to find the number that needs to be added to a fraction and a fraction with a variable denominator and a variable numerator?

A: Yes, you can use this method to find the number that needs to be added to a fraction and a fraction with a variable denominator and a variable numerator. As long as you find the common denominator and subtract the numerators while keeping the denominators the same, you will arrive at the correct answer.

This method is applicable to any combination of fractions and fractions with variable denominators and variable numerators.

Q: What if I have a fraction with a negative variable denominator and a negative variable numerator?

A: If you have a fraction with a negative variable denominator and a negative variable numerator, you can still find the number that needs to be added. Simply substitute the variables with values and then proceed with the calculation.

Substituting the variables with values will allow you to work with whole numbers, making the calculation easier.

Q: Can I use this method to find the number that needs to be added to a fraction and a fraction with a negative variable denominator and a negative variable numerator?

A: Yes, you can use this method to find the number that needs to be added to a fraction and a fraction with a negative variable denominator and a negative variable numerator. As long as you find the common denominator and subtract the numerators while keeping the denominators the same, you will arrive at the correct answer.

This method is applicable to any combination of fractions and fractions with negative variable denominators and negative variable numerators.

Q: What if I have a fraction with a variable numerator and a variable denominator, and the variables are related by an equation?

A: If you have a fraction with a variable numerator and a variable denominator, and the variables are related by an equation, you can still find the number that needs to be added. Simply substitute the variables with values and then proceed with the calculation.

Substituting the variables with values will allow you to work with whole numbers, making the calculation easier.

Q: Can I use this method to find the number that needs to be added to a fraction and a fraction with a variable numerator and a variable denominator, and the variables are related by an equation?

A: Yes, you can use this method to find the number that needs to be added to a fraction and a fraction with a variable numerator and a variable denominator, and the variables are related by an equation. As long as you find the common denominator and subtract the numerators while keeping the denominators the same, you will arrive at the correct answer.

This method is applicable to any combination of fractions and fractions with variable numerators and variable denominators, and the variables are related by an equation.

Q: What if I have a fraction with a negative variable numerator and a variable denominator, and the variables are related by an equation?

A: If you have a fraction with a negative variable numerator and a variable denominator, and the variables are related by an equation, you can still find the number that needs to be added. Simply substitute the variables with values