What Is 168/25 Simplified Fraction? Step-By-Step Explanation

Understanding fractions and their simplification is essential in mathematics. Simplification refers to reducing a fraction to its simplest form, where the numerator and denominator no longer have common factors. In this article, we’ll walk you …

What Is 168/25 Simplified Fraction

Understanding fractions and their simplification is essential in mathematics. Simplification refers to reducing a fraction to its simplest form, where the numerator and denominator no longer have common factors. In this article, we’ll walk you through the process of simplifying the What Is 168/25 Simplified Fraction, providing a step-by-step guide and useful explanations to make the process easy to understand.

We will also provide helpful information about fractions, their importance in real-world applications, and answer five frequently asked questions (FAQs) about fraction simplification.

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What Does It Mean To Simplify A Fraction?

Before diving into the specific example of 168/25, it’s important to understand what it means to simplify a fraction. A fraction is a mathematical expression representing a part of a whole, consisting of two numbers: a numerator (top number) and a denominator (bottom number). Simplification involves reducing the fraction to its simplest form, which means that the greatest common divisor (GCD) of the numerator and denominator is 1.

For example, the fraction 168/25 can be simplified if both numbers share common factors, other than 1. The goal is to divide both the numerator and the denominator by their GCD.

Key Terms to Know

  1. Fraction: A number expressed as the ratio of two integers, where the top number is the numerator, and the bottom number is the denominator.
  2. Simplification: The process of reducing a fraction to its simplest form.
  3. Greatest Common Divisor (GCD): The largest number that divides both the numerator and the denominator without leaving a remainder.

Now, let’s break down how to simplify 168/25 in a systematic way.

Step-by-Step Process Of Simplifying 168/25

Step 1: Find the Greatest Common Divisor (GCD)

The first step in simplifying any fraction is to find the GCD of the numerator and denominator. For 168/25, we need to determine the largest number that divides both 168 and 25 evenly.

Divisors of 168

168 can be factored as follows:

168=2×2×2×3×7168 = 2 \times 2 \times 2 \times 3 \times 7

The divisors of 168 are: 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, and 168.

Divisors of 25

Since 25 is a perfect square, its divisors are:

25=5×525 = 5 \times 5

The divisors of 25 are: 1, 5, and 25.

Step 2: Identify the Greatest Common Divisor

Next, we compare the divisors of 168 and 25. The only common divisor between them is 1. This means that 168 and 25 do not have any common factors other than 1.

Step 3: Simplify the Fraction

Since the GCD of 168 and 25 is 1, the fraction is already in its simplest form. Therefore, 168/25 cannot be simplified further.

The simplified fraction is:

16825\frac{168}{25}

Step 4: Convert to a Mixed Number (Optional)

While 168/25 cannot be simplified further, it can be converted into a mixed number for easier understanding. To do this, divide 168 by 25.

168÷25=6 remainder 18168 \div 25 = 6 \text{ remainder } 18

This means that 168/25 can be written as:

618256 \frac{18}{25}

So, 168/25 as a mixed number is 6 18/25.

Real-World Applications Of Simplifying Fractions

Simplifying fractions is not just a theoretical exercise. It has real-world applications that make it easier to solve practical problems. Here are some examples:

Cooking: Recipes often require measurements in fractions. Simplifying fractions makes it easier to adjust recipes and scale ingredients according to the number of servings.

Finance: When dealing with interest rates, loans, or tax calculations, simplified fractions help in making quick calculations and understanding percentages.

Construction and Engineering: Fractions are used to measure lengths, areas, and volumes. Simplifying these fractions helps in creating accurate measurements for building projects.

Conclusion

To summarize, the fraction 168/25 is already in its simplest form because the greatest common divisor (GCD) between the numerator and denominator is 1. Simplifying fractions is an important skill in mathematics that helps you make calculations easier and more efficient. In this case, 168/25 can also be expressed as the mixed number 6 18/25.

By following the steps outlined above, you can simplify other fractions in a similar manner. Whether you’re working on academic problems, cooking, or handling finances, understanding how to simplify fractions will make your life easier.

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FAQs

What is a Simplified Fraction?

A simplified fraction is a fraction where the numerator and denominator are as small as possible and have no common divisors other than 1. In other words, the greatest common divisor (GCD) of the numerator and denominator is 1.

How Do You Simplify a Fraction?

To simplify a fraction, you need to divide both the numerator and the denominator by their greatest common divisor (GCD). Once you divide by the GCD, the fraction will be in its simplest form.

Can All Fractions Be Simplified?

No, not all fractions can be simplified. If the numerator and denominator are already prime numbers or have no common factors other than 1, the fraction cannot be simplified any further.

What Is the Simplified Fraction of 168/25?

The fraction 168/25 is already in its simplest form because the greatest common divisor (GCD) of 168 and 25 is 1.

How Do You Convert a Fraction Into a Mixed Number?

To convert a fraction into a mixed number, divide the numerator by the denominator. The quotient becomes the whole number, and the remainder becomes the new numerator, with the original denominator remaining the same.

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