Subtract. Write Your Answer As A Fraction In Simplest Form.$\frac{7}{12} - \frac{5}{12}$

Introduction

When it comes to subtracting fractions, it's essential to understand the concept of like and unlike denominators. In this article, we will delve into the world of fractions and explore the process of subtracting two fractions with the same denominator. We will also provide a step-by-step guide on how to simplify the resulting fraction.

Understanding Like and Unlike Denominators

Before we dive into the process of subtracting fractions, it's crucial to understand the concept of like and unlike denominators. A like denominator is a common denominator shared by two or more fractions, while an unlike denominator is a denominator that is not shared by two or more fractions.

Like Denominators

When two or more fractions have the same denominator, they are said to have like denominators. For example, the fractions $\frac{1}{4}$ and $\frac{2}{4}$ have like denominators because they share the same denominator, which is 4.

Unlike Denominators

On the other hand, when two or more fractions do not share the same denominator, they are said to have unlike denominators. For example, the fractions $\frac{1}{4}$ and $\frac{2}{5}$ have unlike denominators because they do not share the same denominator.

Subtracting Fractions with Like Denominators

Now that we have a good understanding of like and unlike denominators, let's move on to the process of subtracting fractions with like denominators. The process is relatively straightforward and involves subtracting the numerators while keeping the denominator the same.

Example 1: Subtracting Fractions with Like Denominators

Let's consider the following example: $\frac{7}{12} - \frac{5}{12}$. In this example, both fractions have the same denominator, which is 12. To subtract these fractions, we simply subtract the numerators while keeping the denominator the same.

$\frac{7}{12} - \frac{5}{12} = \frac{7-5}{12} = \frac{2}{12}$

Simplifying the Resulting Fraction

Now that we have subtracted the fractions, we need to simplify the resulting fraction. To simplify a fraction, we need to find the greatest common divisor (GCD) of the numerator and the denominator and divide both numbers by the GCD.

In this case, the GCD of 2 and 12 is 2. Therefore, we can simplify the fraction by dividing both numbers by 2.

$\frac{2}{12} = \frac{2 \div 2}{12 \div 2} = \frac{1}{6}$

Conclusion

In conclusion, subtracting fractions with like denominators is a straightforward process that involves subtracting the numerators while keeping the denominator the same. By following the steps outlined in this article, you can simplify fractions and arrive at the correct answer.

Frequently Asked Questions

• Q: What is the difference between like and unlike denominators? A: Like denominators are common denominators shared by two or more fractions, while unlike denominators are denominators that are not shared by two or more fractions.
• Q: How do I subtract fractions with like denominators? A: To subtract fractions with like denominators, simply subtract the numerators while keeping the denominator the same.
• Q: How do I simplify a fraction? A: To simplify a fraction, find the greatest common divisor (GCD) of the numerator and the denominator and divide both numbers by the GCD.

Final Answer

The final answer to the problem $\frac{7}{12} - \frac{5}{12}$ is $\boxed{\frac{1}{6}}$.

Introduction

In our previous article, we explored the concept of subtracting fractions with like denominators. We provided a step-by-step guide on how to simplify fractions and arrive at the correct answer. In this article, we will continue to provide more information and answer frequently asked questions related to subtracting fractions.

Q&A: Subtracting Fractions

Q: What is the difference between subtracting fractions and adding fractions?

A: Subtracting fractions involves finding the difference between two or more fractions, while adding fractions involves finding the sum of two or more fractions. The process of subtracting fractions is similar to adding fractions, but with a negative sign.

Q: How do I subtract fractions with unlike denominators?

A: To subtract fractions with unlike denominators, you need to find the least common multiple (LCM) of the two denominators. Then, multiply both fractions by the LCM to create equivalent fractions with the same denominator. Finally, subtract the numerators while keeping the denominator the same.

Q: What is the least common multiple (LCM)?

A: The least common multiple (LCM) is the smallest multiple that two or more numbers have in common. For example, the LCM of 4 and 6 is 12.

Q: How do I find the LCM of two numbers?

A: To find the LCM of two numbers, list the multiples of each number and find the smallest multiple that appears in both lists. Alternatively, you can use the prime factorization method to find the LCM.

Q: What is the prime factorization method?

A: The prime factorization method involves breaking down each number into its prime factors and then multiplying the prime factors together to find the LCM.

Q: How do I multiply fractions?

A: To multiply fractions, multiply the numerators together and multiply the denominators together. Then, simplify the resulting fraction by dividing both numbers by the greatest common divisor (GCD).

Q: What is the greatest common divisor (GCD)?

A: The greatest common divisor (GCD) is the largest number that two or more numbers have in common. For example, the GCD of 12 and 18 is 6.

Q: How do I simplify a fraction?

A: To simplify a fraction, find the greatest common divisor (GCD) of the numerator and the denominator and divide both numbers by the GCD.

Q: What is the difference between a proper fraction and an improper fraction?

A: A proper fraction is a fraction where the numerator is less than the denominator, while an improper fraction is a fraction where the numerator is greater than or equal to the denominator.

Q: How do I convert a proper fraction to an improper fraction?

A: To convert a proper fraction to an improper fraction, multiply the numerator and the denominator by the same number. For example, to convert $\frac{3}{4}$ to an improper fraction, multiply the numerator and the denominator by 4.

Q: How do I convert an improper fraction to a proper fraction?

A: To convert an improper fraction to a proper fraction, divide the numerator by the denominator. For example, to convert $\frac{7}{4}$ to a proper fraction, divide the numerator by the denominator.

Conclusion

In conclusion, subtracting fractions is a straightforward process that involves finding the difference between two or more fractions. By following the steps outlined in this article, you can simplify fractions and arrive at the correct answer. Remember to always find the least common multiple (LCM) of the two denominators and multiply both fractions by the LCM to create equivalent fractions with the same denominator.

Frequently Asked Questions

• Q: What is the difference between subtracting fractions and adding fractions? A: Subtracting fractions involves finding the difference between two or more fractions, while adding fractions involves finding the sum of two or more fractions.
• Q: How do I subtract fractions with unlike denominators? A: To subtract fractions with unlike denominators, you need to find the least common multiple (LCM) of the two denominators and multiply both fractions by the LCM to create equivalent fractions with the same denominator.
• Q: What is the least common multiple (LCM)? A: The least common multiple (LCM) is the smallest multiple that two or more numbers have in common.

Final Answer

The final answer to the problem $\frac{7}{12} - \frac{5}{12}$ is $\boxed{\frac{1}{6}}$.