Simplifying 42/66: A Step-By-Step Guide

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Reducing fractions to their simplest form is an essential math skill that can be a bit tricky, but with a step-by-step approach, you'll be a pro in no time. In this article, we'll take the fraction 42/66 and simplify it to its lowest terms.

Understanding the Concept of Simplifying Fractions

Simplifying fractions involves finding the greatest common divisor (GCD) of the numerator and denominator and dividing both numbers by the GCD. This process reduces the fraction to its simplest form, making it easier to work with.

Step 1: Find the Greatest Common Divisor (GCD)

To simplify the fraction 42/66, we need to find the GCD of 42 and 66. We can do this by listing the factors of each number:

• Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
• Factors of 66: 1, 2, 3, 6, 11, 22, 33, 66

The greatest common divisor of 42 and 66 is 6.

Step 2: Divide the Numerator and Denominator by the GCD

Now that we have the GCD, we can divide both the numerator and denominator by 6:

42 ÷ 6 = 7 66 ÷ 6 = 11

So, the simplified fraction is 7/11.

Benefits of Simplifying Fractions

Simplifying fractions has several benefits, including:

• Making calculations easier: Simplified fractions are easier to work with, especially when performing arithmetic operations like addition, subtraction, multiplication, and division.
• Reducing errors: Simplifying fractions reduces the risk of errors, as it eliminates unnecessary calculations and makes it easier to spot mistakes.
• Improving understanding: Simplifying fractions helps to build a deeper understanding of mathematical concepts, as it requires an understanding of factors, multiples, and equivalent ratios.

Real-World Applications of Simplifying Fractions

Simplifying fractions has numerous real-world applications, including:

• Cooking and recipes: Simplifying fractions is essential when scaling recipes up or down, as it ensures that the ingredient ratios remain consistent.
• Finance and accounting: Simplifying fractions is used in financial calculations, such as determining interest rates, investment returns, and tax rates.
• Science and engineering: Simplifying fractions is crucial in scientific and engineering applications, such as calculating proportions, ratios, and percentages.

Conclusion

Simplifying fractions is a fundamental math skill that has numerous benefits and applications. By following the step-by-step approach outlined in this article, you can simplify the fraction 42/66 to its lowest terms, making it easier to work with and understand. Remember to always find the greatest common divisor and divide both the numerator and denominator by the GCD to simplify fractions.