Simplify 68 As A Fraction In 3 Easy Steps

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Simplify 68 As A Fraction In 3 Easy Steps

Simplifying fractions is a crucial skill in mathematics, and it's used in various mathematical operations, such as addition, subtraction, multiplication, and division. In this article, we will show you how to simplify 68 as a fraction in three easy steps.

First, we need to understand that a fraction is a way to represent a part of a whole. It consists of two numbers: the numerator and the denominator. The numerator is the top number, and the denominator is the bottom number. For example, in the fraction 68/100, 68 is the numerator, and 100 is the denominator.

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.

Step 1: Find the Greatest Common Divisor (GCD)

To find the GCD of 68 and 100, we can use the following methods:

• List the factors of 68: 1, 2, 4, 17, 34, 68
• List the factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
• Identify the common factors: 1, 2, 4
• Choose the largest common factor: 4

So, the GCD of 68 and 100 is 4.

Why is Finding the GCD Important?

Finding the GCD is important because it helps us simplify the fraction. By dividing both the numerator and the denominator by the GCD, we can reduce the fraction to its simplest form.

Step 2: Divide the Numerator and the Denominator by the GCD

Now that we have found the GCD, we can simplify the fraction 68/100.

• Divide the numerator (68) by the GCD (4): 68 ÷ 4 = 17
• Divide the denominator (100) by the GCD (4): 100 ÷ 4 = 25

The simplified fraction is 17/25.

Example Problem: Simplify the Fraction 24/36

To simplify the fraction 24/36, we need to find the GCD of 24 and 36.

• List the factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
• List the factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
• Identify the common factors: 1, 2, 3, 4, 6, 12
• Choose the largest common factor: 12

So, the GCD of 24 and 36 is 12.

• Divide the numerator (24) by the GCD (12): 24 ÷ 12 = 2
• Divide the denominator (36) by the GCD (12): 36 ÷ 12 = 3

The simplified fraction is 2/3.

Step 3: Check if the Fraction Can Be Simplified Further

Sometimes, the fraction can be simplified further. To check if the fraction 17/25 can be simplified further, we need to find the GCD of 17 and 25.

• List the factors of 17: 1, 17
• List the factors of 25: 1, 5, 25
• Identify the common factors: 1
• Choose the largest common factor: 1

Since the GCD of 17 and 25 is 1, the fraction 17/25 cannot be simplified further.

Real-World Application of Simplifying Fractions

Simplifying fractions is used in various real-world applications, such as:

• Cooking: When following a recipe, you may need to simplify fractions to measure ingredients accurately.
• Science: Scientists use fractions to represent data and simplify them to make it easier to understand.
• Finance: Fractions are used to represent interest rates and simplify them to calculate interest.

In conclusion, simplifying fractions is an essential skill in mathematics, and it's used in various real-world applications. By following the three easy steps outlined in this article, you can simplify fractions with ease.

We hope this article has helped you understand how to simplify fractions in three easy steps. If you have any questions or need further clarification, please don't hesitate to ask.