What Is The Simplified Form Of The Fraction Below? 5 15 \frac{5}{15} 15 5 ​ A. 1 3 \frac{1}{3} 3 1 ​ B. 1 2 \frac{1}{2} 2 1 ​ C. 1 10 \frac{1}{10} 10 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 $\frac{5}{15}$ and provide a step-by-step guide on how to simplify fractions in general.

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.

Simplifying the Fraction $\frac{5}{15}$

To simplify the fraction $\frac{5}{15}$, we need to find the greatest common divisor (GCD) of the numerator and denominator. The GCD is the largest number that divides both numbers without leaving a remainder.

Step 1: Find the Greatest Common Divisor (GCD)

To find the GCD of 5 and 15, we can list the factors of each number:

• Factors of 5: 1, 5
• Factors of 15: 1, 3, 5, 15

The greatest common divisor of 5 and 15 is 5.

Step 2: Divide the Numerator and Denominator by the GCD

Now that we have found the GCD, we can divide the numerator and denominator by 5:

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

Conclusion

The simplified form of the fraction $\frac{5}{15}$ is $\frac{1}{3}$. This is because the numerator and denominator have a common factor of 5, which we divided out to simplify the fraction.

Simplifying Fractions: A General Guide

Simplifying fractions is a straightforward process that involves finding the greatest common divisor of the numerator and denominator and dividing both numbers by it. Here are the steps to simplify a fraction:

1. Find the greatest common divisor (GCD) of the numerator and denominator.
2. Divide the numerator and denominator by the GCD.
3. Write the resulting fraction as the simplified form.

Example 1: Simplifying the Fraction $\frac{12}{18}$

To simplify the fraction $\frac{12}{18}$, we need to find the GCD of 12 and 18. The factors of 12 are 1, 2, 3, 4, 6, and 12, while the factors of 18 are 1, 2, 3, 6, 9, and 18. The greatest common divisor of 12 and 18 is 6.

Now that we have found the GCD, we can divide the numerator and denominator by 6:

$\frac{12}{18} = \frac{12 ÷ 6}{18 ÷ 6} = \frac{2}{3}$

Example 2: Simplifying the Fraction $\frac{20}{30}$

To simplify the fraction $\frac{20}{30}$, we need to find the GCD of 20 and 30. The factors of 20 are 1, 2, 4, 5, 10, and 20, while the factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30. The greatest common divisor of 20 and 30 is 10.

Now that we have found the GCD, we can divide the numerator and denominator by 10:

$\frac{20}{30} = \frac{20 ÷ 10}{30 ÷ 10} = \frac{2}{3}$

Conclusion

Simplifying fractions is a crucial skill in mathematics, and it involves finding the greatest common divisor of the numerator and denominator and dividing both numbers by it. By following the steps outlined in this article, you can simplify fractions with ease and master this essential math skill.

Common Mistakes to Avoid

When simplifying fractions, it's essential to avoid common mistakes that can lead to incorrect answers. Here are some common mistakes to avoid:

• Not finding the greatest common divisor (GCD) of the numerator and denominator.
• Dividing the numerator and denominator by a number that is not the GCD.
• Not simplifying the fraction to its lowest terms.

Conclusion

Introduction

Simplifying fractions is a fundamental concept in mathematics, and it's essential to understand how to simplify fractions to master this skill. In this article, we'll provide a Q&A guide to help you understand the basics of simplifying fractions and address common questions and concerns.

Q: What is a simplified fraction?

A: 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.

Q: How do I simplify a fraction?

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

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

A: The greatest common divisor (GCD) is the largest number that divides both numbers without leaving a remainder.

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

A: To find the GCD of two numbers, you can list the factors of each number and find the largest number that is common to both lists.

Q: What if the GCD is 1?

A: If the GCD is 1, then the fraction is already in its simplest form.

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

A: No, you cannot simplify a fraction with a zero numerator or denominator. In this case, the fraction is undefined.

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

A: Yes, you can simplify a fraction with a negative numerator or denominator. The sign of the numerator and denominator will be preserved in the simplified fraction.

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

A: To simplify a fraction with a variable numerator or denominator, you need to find the greatest common divisor (GCD) of the variable and the constant terms and divide both numbers by it.

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. In this case, the fraction is already in its simplest form.

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

A: To simplify a fraction with a mixed number numerator or denominator, you need to convert the mixed number to an improper fraction and then simplify the fraction.

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

A: Yes, you can simplify a fraction with a complex numerator or denominator. The process is similar to simplifying a fraction with a variable numerator or denominator.

Conclusion

In conclusion, simplifying fractions is a straightforward process that involves finding the greatest common divisor (GCD) of the numerator and denominator and dividing both numbers by it. By following the steps outlined in this article, you can simplify fractions with ease and master this essential math skill. Remember to address common questions and concerns, and you'll be well on your way to becoming a math whiz.

Common Mistakes to Avoid

When simplifying fractions, it's essential to avoid common mistakes that can lead to incorrect answers. Here are some common mistakes to avoid:

• Not finding the greatest common divisor (GCD) of the numerator and denominator.
• Dividing the numerator and denominator by a number that is not the GCD.
• Not simplifying the fraction to its lowest terms.
• Simplifying a fraction with a zero numerator or denominator.
• Simplifying a fraction with a decimal numerator or denominator.

Conclusion

In conclusion, simplifying fractions is a fundamental concept in mathematics, and it's essential to understand how to simplify fractions to master this skill. By following the steps outlined in this article and addressing common questions and concerns, you can simplify fractions with ease and become a math whiz.