Simplify The Fraction 12 150 \frac{12}{150} 150 12 ​ .

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Introduction

Simplifying fractions is an essential skill in mathematics, and it's often used in various mathematical operations, such as adding, subtracting, multiplying, and dividing fractions. In this article, we will focus on simplifying the fraction $\frac{12}{150}$ using the concept of greatest common divisor (GCD). We will also explore other methods to simplify fractions, including factoring and canceling common factors.

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. For example, the fraction $\frac{6}{8}$ can be simplified to $\frac{3}{4}$ because 6 and 8 have a common factor of 2.

Method 1: Greatest Common Divisor (GCD)

To simplify the fraction $\frac{12}{150}$ using the GCD method, we need to find the greatest common divisor of 12 and 150. The GCD is the largest number that divides both numbers without leaving a remainder. We can use the Euclidean algorithm to find the GCD.

Step 1: Find the GCD of 12 and 150

To find the GCD of 12 and 150, we can use the Euclidean algorithm:

150 = 12 × 12 + 6 12 = 6 × 2 + 0

The last non-zero remainder is 6, so the GCD of 12 and 150 is 6.

Step 2: Simplify the Fraction

Now that we have found the GCD, we can simplify the fraction $\frac{12}{150}$ by dividing both the numerator and denominator by the GCD:

$\frac{12}{150} = \frac{12 ÷ 6}{150 ÷ 6} = \frac{2}{25}$

Method 2: Factoring

Another method to simplify fractions is by factoring the numerator and denominator. We can factor 12 and 150 as follows:

12 = 2 × 2 × 3 150 = 2 × 3 × 5 × 5

We can see that both 12 and 150 have a common factor of 2 × 3 = 6. We can cancel out this common factor to simplify the fraction:

$\frac{12}{150} = \frac{2 × 2 × 3}{2 × 3 × 5 × 5} = \frac{2}{5 × 5} = \frac{2}{25}$

Method 3: Canceling Common Factors

We can also simplify fractions by canceling common factors. We can see that both 12 and 150 have a common factor of 6. We can cancel out this common factor to simplify the fraction:

$\frac{12}{150} = \frac{2 × 6}{5 × 5 × 6} = \frac{2}{5 × 5} = \frac{2}{25}$

Conclusion

In this article, we have explored three methods to simplify the fraction $\frac{12}{150}$: the greatest common divisor (GCD) method, factoring, and canceling common factors. We have seen that all three methods lead to the same simplified fraction: $\frac{2}{25}$. Simplifying fractions is an essential skill in mathematics, and it's often used in various mathematical operations. By mastering the art of simplifying fractions, we can solve mathematical problems more efficiently and effectively.

Frequently Asked Questions

• 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.
• How do I simplify a fraction using the GCD method? To simplify a fraction using the GCD method, you need to find the greatest common divisor of the numerator and denominator, and then divide both the numerator and denominator by the GCD.
• How do I simplify a fraction using factoring? To simplify a fraction using factoring, you need to factor the numerator and denominator, and then cancel out any common factors.
• How do I simplify a fraction using canceling common factors? To simplify a fraction using canceling common factors, you need to identify any common factors between the numerator and denominator, and then cancel them out.

Further Reading

• Greatest Common Divisor (GCD)
• Factoring
• Canceling Common Factors
• Simplifying Fractions
• Mathematical Operations
  

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Introduction

In our previous article, we explored three methods to simplify the fraction $\frac{12}{150}$: the greatest common divisor (GCD) method, factoring, and canceling common factors. In this article, we will answer some frequently asked questions (FAQs) related to simplifying fractions.

Q&A

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 using the GCD method?

A: To simplify a fraction using the GCD method, you need to find the greatest common divisor of the numerator and denominator, and then divide both the numerator and denominator by the GCD.

Q: How do I simplify a fraction using factoring?

A: To simplify a fraction using factoring, you need to factor the numerator and denominator, and then cancel out any common factors.

Q: How do I simplify a fraction using canceling common factors?

A: To simplify a fraction using canceling common factors, you need to identify any common factors between the numerator and denominator, and then cancel them out.

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: You can use the Euclidean algorithm to find the GCD of two numbers. The Euclidean algorithm is a step-by-step process that involves dividing the larger number by the smaller number, and then replacing the larger number with the remainder.

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. To simplify a fraction with a negative numerator or denominator, you need to follow the same steps as simplifying a fraction with positive numbers.

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

A: Yes, you can simplify a fraction with a decimal numerator or denominator. To simplify a fraction with a decimal numerator or denominator, you need to convert the decimal to a fraction, and then simplify the 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 follow the same steps as simplifying a fraction with positive numbers. However, you may need to use algebraic manipulations to simplify the fraction.

Conclusion

In this article, we have answered some frequently asked questions (FAQs) related to simplifying fractions. We have covered topics such as the greatest common divisor (GCD) method, factoring, canceling common factors, and simplifying fractions with negative, decimal, and variable numerators or denominators. By mastering the art of simplifying fractions, you can solve mathematical problems more efficiently and effectively.

Further Reading

• Greatest Common Divisor (GCD)
• Factoring
• Canceling Common Factors
• Simplifying Fractions
• Mathematical Operations
• Algebraic Manipulations

Additional Resources

• Khan Academy: Simplifying Fractions
• Mathway: Simplifying Fractions
• Wolfram Alpha: Simplifying Fractions

Glossary

• Greatest Common Divisor (GCD): The largest number that divides both numbers without leaving a remainder.
• Factoring: The process of expressing a number as a product of its prime factors.
• Canceling Common Factors: The process of canceling out common factors between the numerator and denominator.
• Simplified Fraction: A fraction that has been reduced to its lowest terms, meaning that the numerator and denominator have no common factors other than 1.