What Is The Simplified Form Of The Fraction Below? 6 24 \frac{6}{24} 24 6 ​ A. 1 4 \frac{1}{4} 4 1 ​ B. 1 3 \frac{1}{3} 3 1 ​ C. 1 8 \frac{1}{8} 8 1 ​ D. 1 6 \frac{1}{6} 6 1 ​

Introduction

Fractions are a fundamental concept in mathematics, and simplifying them is an essential skill to master. In this article, we will explore the simplified form of the fraction $\frac{6}{24}$ and provide a step-by-step guide on how to simplify fractions.

What is a Simplified Fraction?

A simplified fraction is a fraction that has been reduced to its lowest terms, meaning that the numerator and denominator have no common factors other than 1. In other words, a simplified fraction is a fraction that cannot be reduced further.

Why Simplify Fractions?

Simplifying fractions is important because it makes calculations easier and more efficient. When fractions are simplified, it is easier to compare them, add or subtract them, and perform other mathematical operations.

Step-by-Step Guide to Simplifying Fractions

To simplify a fraction, follow these steps:

1. Find the Greatest Common Divisor (GCD): The GCD is the largest number that divides both the numerator and denominator without leaving a remainder. To find the GCD, list the factors of the numerator and denominator and find the greatest common factor.
2. Divide the Numerator and Denominator by the GCD: Once you have found the GCD, divide both the numerator and denominator by the GCD to simplify the fraction.
3. Check if the Fraction Can Be Reduced Further: After simplifying the fraction, check if it can be reduced further by finding the GCD of the new numerator and denominator.

Simplifying the Fraction $\frac{6}{24}$

To simplify the fraction $\frac{6}{24}$, follow the steps outlined above:

1. Find the Greatest Common Divisor (GCD): The factors of 6 are 1, 2, 3, and 6. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. The greatest common factor of 6 and 24 is 6.
2. Divide the Numerator and Denominator by the GCD: Divide both the numerator and denominator by 6 to simplify the fraction: $\frac{6}{24} = \frac{1}{4}$.
3. Check if the Fraction Can Be Reduced Further: After simplifying the fraction, check if it can be reduced further by finding the GCD of the new numerator and denominator. In this case, the GCD of 1 and 4 is 1, so the fraction $\frac{1}{4}$ cannot be reduced further.

Conclusion

In conclusion, simplifying fractions is an essential skill in mathematics that makes calculations easier and more efficient. By following the steps outlined above, you can simplify fractions and reduce them to their lowest terms.

Common Mistakes to Avoid

When simplifying fractions, there are several common mistakes to avoid:

• Not finding the GCD: Failing to find the GCD can result in an unsimplified fraction.
• Not dividing the numerator and denominator by the GCD: Failing to divide both the numerator and denominator by the GCD can result in an unsimplified fraction.
• Not checking if the fraction can be reduced further: Failing to check if the fraction can be reduced further can result in an unsimplified fraction.

Practice Problems

To practice simplifying fractions, try the following problems:

• Simplify the fraction $\frac{8}{16}$.
• Simplify the fraction $\frac{12}{24}$.
• Simplify the fraction $\frac{15}{30}$.

Answer Key

• $\frac{8}{16} = \frac{1}{2}$
• $\frac{12}{24} = \frac{1}{2}$
• $\frac{15}{30} = \frac{1}{2}$

Conclusion

Q: What is the greatest common divisor (GCD) and why is it important in simplifying fractions?

A: The greatest common divisor (GCD) is the largest number that divides both the numerator and denominator without leaving a remainder. It is important in simplifying fractions because it helps to reduce the fraction to its lowest terms.

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

A: To find the GCD of two numbers, list the factors of each number and find the greatest common factor. For example, to find the GCD of 6 and 24, list the factors of each number:

• Factors of 6: 1, 2, 3, 6
• Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

The greatest common factor of 6 and 24 is 6.

Q: How do I simplify a fraction using the GCD?

A: To simplify a fraction using the GCD, follow these steps:

1. Find the GCD of the numerator and denominator.
2. Divide both the numerator and denominator by the GCD.
3. Check if the fraction can be reduced further by finding the GCD of the new numerator and denominator.

Q: What is the difference between simplifying a fraction and reducing a fraction?

A: Simplifying a fraction means reducing it to its lowest terms by dividing both the numerator and denominator by their greatest common divisor. Reducing a fraction means finding the greatest common divisor of the numerator and denominator and dividing both by that number.

Q: Can a fraction be simplified if the numerator and denominator have no common factors?

A: Yes, a fraction can be simplified even if the numerator and denominator have no common factors. In this case, the fraction is already in its simplest form.

Q: How do I know if a fraction is in its simplest form?

A: A fraction is in its simplest form if the numerator and denominator have no common factors other than 1.

Q: Can a fraction be simplified if the numerator and denominator are both prime numbers?

A: Yes, a fraction can be simplified even if the numerator and denominator are both prime numbers. In this case, the fraction is already in its simplest form.

Q: What is the importance of simplifying fractions in real-life situations?

A: Simplifying fractions is important in real-life situations because it makes calculations easier and more efficient. For example, in cooking, simplifying fractions can help you measure ingredients accurately. In finance, simplifying fractions can help you calculate interest rates and investments more easily.

Q: Can I use a calculator to simplify fractions?

A: Yes, you can use a calculator to simplify fractions. However, it is still important to understand the concept of simplifying fractions and how to do it manually.

Q: How do I simplify a fraction with a negative numerator or denominator?

A: To simplify a fraction with a negative numerator or denominator, follow the same steps as simplifying a fraction with positive numbers. The negative sign will be carried over to the simplified fraction.

Q: Can I simplify a fraction with a decimal numerator or denominator?

A: No, you cannot simplify a fraction with a decimal numerator or denominator. Decimals are a different form of representation and cannot be simplified in the same way as fractions.

Conclusion

In conclusion, simplifying fractions is an essential skill in mathematics that makes calculations easier and more efficient. By understanding the concept of simplifying fractions and how to do it manually, you can apply it to real-life situations and make calculations more accurate and efficient.