Simplifying 625/100: A Step-By-Step Guide

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Reducing fractions to their simplest form is an essential skill in mathematics, and it's a concept that can be applied in various real-world situations. In this article, we'll focus on simplifying the fraction 625/100. By the end of this guide, you'll have a clear understanding of the steps involved in simplifying this fraction and be able to apply this knowledge to other similar problems.

Simplifying fractions involves finding the greatest common divisor (GCD) of the numerator and the denominator and dividing both numbers by the GCD. The result is a fraction that is equivalent to the original fraction but in its simplest form.

Step 1: Find the Greatest Common Divisor (GCD)

To simplify the fraction 625/100, we need to find the greatest common divisor (GCD) of 625 and 100. The GCD is the largest number that divides both numbers without leaving a remainder. We can find the GCD using various methods, including prime factorization, the Euclidean algorithm, or simply listing the factors of each number.

Prime Factorization Method

Using the prime factorization method, we can break down 625 and 100 into their prime factors:

625 = 5 × 5 × 5 × 5 100 = 2 × 2 × 5 × 5

Now, let's identify the common factors:

• 5 is a common factor, and it appears twice in both numbers.

Euclidean Algorithm Method

Alternatively, we can use the Euclidean algorithm to find the GCD. This method involves a series of steps where we repeatedly apply the basic fact that the GCD of two numbers also divides their difference.

625 = 6 × 100 + 25 100 = 4 × 25 + 0

Since the remainder is 0, we can stop here. The GCD is the last non-zero remainder, which is 25.

Step 2: Divide Both Numbers by the GCD

Now that we've found the GCD, which is 25, we can simplify the fraction by dividing both the numerator and the denominator by 25:

625 ÷ 25 = 25 100 ÷ 25 = 4

So, the simplified fraction is 25/4.

Step 3: Check the Answer

To ensure that our answer is correct, we can multiply the numerator and the denominator by the same number, which should give us the original fraction:

25 × 25 = 625 4 × 25 = 100

Indeed, we get the original fraction 625/100.

Practical Applications

Simplifying fractions is a crucial skill in various real-world applications, such as:

• Cooking: When scaling up or down a recipe, you need to simplify fractions to ensure that the ingredient ratios remain the same.
• Science: Fractions are used to express measurements and quantities in various scientific contexts, such as chemistry and physics.
• Finance: Simplifying fractions is essential in finance, particularly when dealing with interest rates, investment returns, and currency exchange rates.

Conclusion

In conclusion, simplifying the fraction 625/100 involves finding the greatest common divisor (GCD) of the numerator and the denominator and dividing both numbers by the GCD. By following the steps outlined in this guide, you can simplify fractions with ease and confidence.

We hope this article has been informative and helpful. If you have any questions or comments, please feel free to share them below.