8/72 In Simplest Form

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Introduction

When dealing with fractions, it's essential to simplify them to their lowest terms. This is because simplified fractions are easier to work with and can help avoid confusion when performing mathematical operations. In this article, we will explore how to simplify the fraction 8/72.

Understanding the Concept of Simplifying Fractions

Simplifying fractions involves finding the greatest common divisor (GCD) of the numerator and the denominator. The GCD is the largest number that divides both the numerator and the denominator without leaving a remainder. Once the GCD is found, it's divided by both the numerator and the denominator to simplify the fraction.

Finding the Greatest Common Divisor (GCD)

To find the GCD of 8 and 72, we need to list the factors of each number.

Factors of 8

  • 1
  • 2
  • 4
  • 8

Factors of 72

  • 1
  • 2
  • 3
  • 4
  • 6
  • 8
  • 9
  • 12
  • 18
  • 24
  • 36
  • 72

Identifying the Greatest Common Divisor

From the list of factors, we can see that the greatest common divisor of 8 and 72 is 8.

Simplifying the Fraction

Now that we have found the GCD, we can simplify the fraction 8/72 by dividing both the numerator and the denominator by the GCD.

Simplified Fraction

8 ÷ 8 = 1 72 ÷ 8 = 9

Therefore, the simplified form of the fraction 8/72 is 1/9.

Conclusion

In conclusion, simplifying fractions is an essential skill in mathematics. By finding the greatest common divisor of the numerator and the denominator, we can simplify fractions to their lowest terms. In this article, we have explored how to simplify the fraction 8/72 and found that its simplified form is 1/9.

Frequently Asked Questions

Q: What is the greatest common divisor (GCD) of 8 and 72?

A: The greatest common divisor of 8 and 72 is 8.

Q: How do I simplify a fraction?

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

Q: What is the simplified form of the fraction 8/72?

A: The simplified form of the fraction 8/72 is 1/9.

Final Thoughts

Simplifying fractions is a crucial concept in mathematics that can help us perform mathematical operations more efficiently. By understanding how to simplify fractions, we can avoid confusion and make calculations easier. In this article, we have explored how to simplify the fraction 8/72 and found that its simplified form is 1/9.

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Introduction

In our previous article, we explored how to simplify the fraction 8/72. We found that the greatest common divisor (GCD) of 8 and 72 is 8, and therefore, the simplified form of the fraction 8/72 is 1/9. In this article, we will answer some frequently asked questions related to simplifying fractions, including the fraction 8/72.

Q&A

Q: What is the greatest common divisor (GCD) of 8 and 72?

A: The greatest common divisor of 8 and 72 is 8.

Q: How do I simplify a fraction?

A: To simplify a fraction, follow these steps:

  1. Find the greatest common divisor (GCD) of the numerator and the denominator.
  2. Divide both the numerator and the denominator by the GCD.
  3. The resulting fraction is the simplified form of the original fraction.

Q: What is the simplified form of the fraction 8/72?

A: The simplified form of the fraction 8/72 is 1/9.

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 process is the same as simplifying a fraction with positive numbers.

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

A: If the numerator is zero, the fraction is equal to zero, and there is no need to simplify it. If the denominator is zero, the fraction is undefined, and it cannot be simplified.

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. However, you need to convert the decimal to a fraction first.

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, convert the mixed number to an improper fraction first, and then simplify the fraction.

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

A: Yes, you can simplify a fraction with a variable numerator or denominator. However, you need to find the greatest common divisor (GCD) of the variable and the other number.

Examples

Example 1: Simplifying a Fraction with a Negative Numerator

Simplify the fraction -8/72.

  • Find the greatest common divisor (GCD) of -8 and 72.
  • The GCD is 8.
  • Divide both the numerator and the denominator by the GCD.
  • -8 ÷ 8 = -1
  • 72 ÷ 8 = 9
  • The simplified form of the fraction -8/72 is -1/9.

Example 2: Simplifying a Fraction with a Zero Numerator

Simplify the fraction 0/72.

  • The numerator is zero, so the fraction is equal to zero.
  • There is no need to simplify it.

Example 3: Simplifying a Fraction with a Decimal Numerator

Simplify the fraction 0.8/72.

  • Convert the decimal to a fraction.
  • 0.8 = 8/10 = 4/5
  • Simplify the fraction 4/5 and 72.
  • Find the greatest common divisor (GCD) of 4 and 72.
  • The GCD is 4.
  • Divide both the numerator and the denominator by the GCD.
  • 4 ÷ 4 = 1
  • 72 ÷ 4 = 18
  • The simplified form of the fraction 0.8/72 is 1/18.

Conclusion

In conclusion, simplifying fractions is an essential skill in mathematics. By understanding how to simplify fractions, we can avoid confusion and make calculations easier. In this article, we have answered some frequently asked questions related to simplifying fractions, including the fraction 8/72. We have also provided examples of how to simplify fractions with negative numerators, zero numerators, decimal numerators, and mixed number numerators.