117/75

Daniel Parker

2 min read

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26-02-2025

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Decoding the Fraction 117/75: Simplifying and Understanding

The fraction 117/75 might seem daunting at first glance, but understanding how to simplify it and interpret its meaning is crucial for various applications, from basic math to more advanced calculations. This article will guide you through the process of simplifying 117/75, explaining the steps and providing context for its value.

1. Simplifying the Fraction:

The core of understanding 117/75 lies in simplifying it to its lowest terms. This means finding the greatest common divisor (GCD) of both the numerator (117) and the denominator (75) and dividing both by that number.

• Finding the GCD: One method is to list the factors of both numbers and identify the largest one they share. Another is to use the Euclidean algorithm, a more efficient method for larger numbers. For 117 and 75, the GCD is 3.

• Simplifying: Now, divide both the numerator and the denominator by the GCD (3):

  117 ÷ 3 = 39 75 ÷ 3 = 25

Therefore, the simplified fraction is 39/25.

2. Converting to a Mixed Number:

While 39/25 is a simplified improper fraction (the numerator is larger than the denominator), it's often helpful to convert it to a mixed number (a whole number and a fraction). To do this:

• Divide: Divide the numerator (39) by the denominator (25): 39 ÷ 25 = 1 with a remainder of 14.

• Express as a Mixed Number: The result is 1 and 14/25. So, 39/25 = 1 14/25.

3. Converting to a Decimal:

Another way to represent 117/75 is as a decimal. This is simply done by dividing the numerator by the denominator:

117 ÷ 75 = 1.56

4. Real-World Applications:

Understanding fractions like 117/75 is essential in many real-world scenarios:

• Measurements: Imagine measuring ingredients for a recipe. If a recipe calls for 117 grams of flour and you only have a scale that measures in 75-gram increments, the fraction helps determine the amount needed.

• Proportions: Fractions are fundamental to understanding proportions and ratios. For example, if you have 117 successes out of 75 attempts, the fraction helps express the success rate.

• Geometry and other fields: Fractions are ubiquitous in various mathematical and scientific fields.

5. Conclusion:

The fraction 117/75, when simplified, becomes 39/25 or the mixed number 1 14/25, or the decimal 1.56. Understanding how to simplify fractions and convert them into different forms is a fundamental skill with broad applications in numerous fields. The ability to easily manipulate fractions makes problem-solving more efficient and accurate. Remember that practice is key to mastering these techniques.