Simplify 24/42 In 3 Easy Steps

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Simplifying fractions can seem daunting, but it's actually a straightforward process. In this article, we'll break down the steps to simplify the fraction 24/42 in a way that's easy to understand.

Understanding Fractions

Before we dive into simplifying 24/42, let's quickly review what fractions are. A fraction is a way to express a part of a whole as a ratio of two numbers. The top number, called the numerator, tells us how many equal parts we have. The bottom number, called the denominator, tells us how many parts the whole is divided into.

Step 1: Find the Greatest Common Divisor (GCD)

To simplify a fraction, we need to find the greatest common divisor (GCD) of the numerator and the denominator. The GCD is the largest number that divides both numbers without leaving a remainder. To find the GCD of 24 and 42, we can list the factors of each number:

• Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
• Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42

The largest number that appears in both lists is 6, so the GCD of 24 and 42 is 6.

Why Do We Need the GCD?

The GCD is essential because it allows us to simplify the fraction by dividing both the numerator and the denominator by the GCD. This process doesn't change the value of the fraction, but it helps us express it in a more straightforward way.

Step 2: Divide the Numerator and Denominator by the GCD

Now that we have the GCD, we can simplify the fraction by dividing both the numerator and the denominator by 6:

• Numerator: 24 ÷ 6 = 4
• Denominator: 42 ÷ 6 = 7

So, the simplified fraction is 4/7.

What If We Didn't Use the GCD?

If we didn't use the GCD, we might simplify the fraction incorrectly. For example, if we divided both numbers by 2, we would get 12/21, which is not the simplest form of the fraction.

Step 3: Check If the Fraction Can Be Simplified Further

Finally, we need to check if the fraction can be simplified further. In this case, the numerator (4) and the denominator (7) have no common factors other than 1, so the fraction is already in its simplest form.

What's the Final Answer?

The simplified fraction of 24/42 is 4/7.

By following these three easy steps, you can simplify any fraction and make it easier to work with. Remember to always find the greatest common divisor, divide the numerator and denominator by the GCD, and check if the fraction can be simplified further.

Now that you know how to simplify fractions, try practicing with different examples. Remember to always follow the three easy steps outlined in this article.