Subtract. 12 25 − 2 5 \frac{12}{25} - \frac{2}{5} 25 12 ​ − 5 2 ​ Remember To Get Common Denominators First. Subtract, Then Simplify If Possible.

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Introduction

When it comes to subtracting fractions, it's essential to have a solid understanding of the concept and the steps involved. In this article, we'll delve into the world of fractions and explore how to subtract them with ease. We'll focus on the problem 1225−25\frac{12}{25} - \frac{2}{5} and provide a step-by-step guide on how to solve it.

Understanding Fractions

Before we dive into the problem, let's take a moment to understand what fractions are. A fraction is a way of expressing a part of a whole. It consists of two parts: the numerator (the top number) and the denominator (the bottom number). The numerator tells us how many equal parts we have, while the denominator tells us how many parts the whole is divided into.

For example, in the fraction 12\frac{1}{2}, the numerator is 1, and the denominator is 2. This means we have 1 equal part out of a total of 2 parts.

Finding Common Denominators

When subtracting fractions, it's crucial to have a common denominator. A common denominator is the least common multiple (LCM) of the two denominators. In other words, it's the smallest number that both denominators can divide into evenly.

Let's find the common denominator for the fractions 1225\frac{12}{25} and 25\frac{2}{5}. To do this, we need to list the multiples of each denominator:

  • Multiples of 25: 25, 50, 75, 100, ...
  • Multiples of 5: 5, 10, 15, 20, 25, ...

As we can see, the least common multiple of 25 and 5 is 25. Therefore, the common denominator for the fractions is 25.

Subtracting Fractions

Now that we have a common denominator, we can subtract the fractions. To do this, we need to subtract the numerators while keeping the denominator the same.

1225−25\frac{12}{25} - \frac{2}{5}

To subtract the fractions, we need to convert the second fraction to have a denominator of 25. We can do this by multiplying the numerator and denominator by 5:

25×55=1025\frac{2}{5} \times \frac{5}{5} = \frac{10}{25}

Now that both fractions have the same denominator, we can subtract the numerators:

1225−1025=225\frac{12}{25} - \frac{10}{25} = \frac{2}{25}

Simplifying the Fraction

The fraction 225\frac{2}{25} cannot be simplified further, as the numerator and denominator have no common factors.

Conclusion

Subtracting fractions may seem daunting at first, but with a solid understanding of the concept and the steps involved, it's a breeze. By finding the common denominator and subtracting the numerators, we can solve even the most complex fraction problems. In this article, we've explored the problem 1225−25\frac{12}{25} - \frac{2}{5} and provided a step-by-step guide on how to solve it.

Frequently Asked Questions

  • Q: What is the common denominator for the fractions 1225\frac{12}{25} and 25\frac{2}{5}? A: The common denominator is 25.
  • Q: How do I subtract fractions with different denominators? A: To subtract fractions with different denominators, you need to find the common denominator and convert both fractions to have the same denominator.
  • Q: Can I simplify the fraction 225\frac{2}{25}? A: No, the fraction 225\frac{2}{25} cannot be simplified further, as the numerator and denominator have no common factors.

Additional Resources

  • Khan Academy: Subtracting Fractions
  • Mathway: Subtracting Fractions
  • IXL: Subtracting Fractions

Final Thoughts

Subtracting fractions is a fundamental concept in mathematics, and with practice and patience, anyone can master it. By following the steps outlined in this article, you'll be able to solve even the most complex fraction problems with ease. Remember to always find the common denominator and subtract the numerators to get the correct answer. Happy calculating!

Introduction

Subtracting fractions can be a challenging concept for many students, but with practice and patience, it can become second nature. In this article, we'll answer some of the most frequently asked questions about subtracting fractions, providing you with a deeper understanding of the concept and helping you to become more confident in your math skills.

Q&A

Q: What is the common denominator for the fractions 1225\frac{12}{25} and 25\frac{2}{5}?

A: The common denominator is 25. To find the common denominator, we need to list the multiples of each denominator and find the least common multiple (LCM). In this case, the multiples of 25 are 25, 50, 75, 100, ... and the multiples of 5 are 5, 10, 15, 20, 25, ... . The least common multiple of 25 and 5 is 25.

Q: How do I subtract fractions with different denominators?

A: To subtract fractions with different denominators, you need to find the common denominator and convert both fractions to have the same denominator. This can be done by multiplying the numerator and denominator of each fraction by the necessary factor to make the denominators equal.

Q: Can I simplify the fraction 225\frac{2}{25}?

A: No, the fraction 225\frac{2}{25} cannot be simplified further, as the numerator and denominator have no common factors. However, you can simplify fractions that have common factors between the numerator and denominator.

Q: What is the difference between subtracting fractions and subtracting mixed numbers?

A: Subtracting fractions involves subtracting the numerators of two fractions with the same denominator, while subtracting mixed numbers involves subtracting the whole number part from the fraction part.

Q: How do I subtract a fraction from a whole number?

A: To subtract a fraction from a whole number, you need to convert the whole number to a fraction with the same denominator as the fraction. Then, you can subtract the numerators.

Q: Can I subtract a negative fraction from a positive fraction?

A: Yes, you can subtract a negative fraction from a positive fraction. When subtracting a negative fraction, you need to change the sign of the fraction and then add it to the positive fraction.

Q: What is the rule for subtracting fractions with unlike denominators?

A: The rule for subtracting fractions with unlike denominators is to find the least common multiple (LCM) of the two denominators and convert both fractions to have the same denominator.

Q: Can I subtract a fraction from a decimal?

A: Yes, you can subtract a fraction from a decimal. To do this, you need to convert the decimal to a fraction with the same denominator as the fraction.

Q: How do I subtract a fraction from a percentage?

A: To subtract a fraction from a percentage, you need to convert the percentage to a decimal and then subtract the fraction.

Conclusion

Subtracting fractions can be a challenging concept, but with practice and patience, it can become second nature. By understanding the common denominator, how to subtract fractions with different denominators, and how to simplify fractions, you'll be able to tackle even the most complex fraction problems with ease. Remember to always find the common denominator and subtract the numerators to get the correct answer.

Additional Resources

  • Khan Academy: Subtracting Fractions
  • Mathway: Subtracting Fractions
  • IXL: Subtracting Fractions

Final Thoughts

Subtracting fractions is a fundamental concept in mathematics, and with practice and patience, anyone can master it. By following the steps outlined in this article and practicing regularly, you'll become more confident in your math skills and be able to tackle even the most complex fraction problems with ease. Happy calculating!