Simplify 39/52: A Step-By-Step Guide To Reduced Fractions

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Simplifying fractions is an essential math skill that can seem daunting at first, but with the right approach, it can become second nature. In this article, we'll take a step-by-step look at how to simplify the fraction 39/52.

Understanding Fractions

Before we dive into simplifying 39/52, let's quickly review what fractions are and how they work. A fraction is a way of expressing a part of a whole as a ratio of two numbers. The top number, known as the numerator, tells us how many equal parts we have, while the bottom number, known as the denominator, tells us how many parts the whole is divided into.

Why Simplify Fractions?

Simplifying fractions is important because it helps us to work with fractions more easily. When we simplify a fraction, we're finding an equivalent fraction that has a smaller numerator and denominator. This makes it easier to add, subtract, multiply, and divide fractions.

Benefits of Simplifying Fractions

Simplifying fractions has several benefits, including:

• Easier calculations: Simplified fractions are easier to work with, making calculations faster and more accurate.
• Reduced errors: Simplifying fractions reduces the chance of errors, as we're working with smaller numbers.
• Improved understanding: Simplifying fractions helps us to better understand the relationships between numbers.

Step-by-Step Guide to Simplifying 39/52

Now that we've covered the basics, let's move on to simplifying 39/52. Here's a step-by-step guide:

Step 1: Find the Greatest Common Divisor (GCD)

The first step in simplifying a fraction is to find the greatest common divisor (GCD) of the numerator and denominator. The GCD is the largest number that divides both numbers evenly.

To find the GCD of 39 and 52, we can use the following steps:

• List the factors of 39: 1, 3, 13, 39
• List the factors of 52: 1, 2, 4, 13, 26, 52
• Identify the common factors: 1, 13
• Choose the largest common factor: 13

Step 2: Divide Both Numbers by the GCD

Now that we've found the GCD, we can simplify the fraction by dividing both numbers by 13.

Numerator: 39 ÷ 13 = 3 Denominator: 52 ÷ 13 = 4

So, the simplified fraction is 3/4.

Example Problems

Let's try a few example problems to practice simplifying fractions:

• Simplify 12/16:
  • Find the GCD: 4
  • Divide both numbers by 4: 12 ÷ 4 = 3, 16 ÷ 4 = 4
  • Simplified fraction: 3/4
• Simplify 24/36:
  • Find the GCD: 12
  • Divide both numbers by 12: 24 ÷ 12 = 2, 36 ÷ 12 = 3
  • Simplified fraction: 2/3

Real-World Applications

Simplifying fractions has many real-world applications, including:

• Cooking: Recipes often involve fractions, and simplifying them can make cooking easier and more efficient.
• Finance: Fractions are used in finance to calculate interest rates, investment returns, and other financial metrics.
• Science: Fractions are used in science to express ratios and proportions, such as the ratio of one substance to another.

Conclusion

Simplifying fractions is an essential math skill that can seem daunting at first, but with the right approach, it can become second nature. By following the step-by-step guide outlined in this article, you can simplify fractions with ease and accuracy. Remember to find the greatest common divisor, divide both numbers by the GCD, and practice with example problems. With practice and patience, you'll become a pro at simplifying fractions in no time!

Take the Next Step

Now that you've learned how to simplify fractions, it's time to take the next step. Practice simplifying fractions with different numbers and apply the skills you've learned to real-world problems. Share your progress with a friend or family member and see how far you can go!

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