What Is 1 6 Of 48

What is 1/6 of 48? A Comprehensive Guide to Fractions and Division

Finding a fraction of a number is a fundamental concept in mathematics, essential for various applications from everyday tasks to complex calculations. This article delves into the question, "What is 1/6 of 48?", providing a step-by-step solution and exploring the broader concept of fraction multiplication and division. We'll cover different methods for solving this problem, emphasizing the underlying mathematical principles and providing practical examples to solidify your understanding.

Understanding Fractions

Before tackling the problem, let's review the basics of fractions. A fraction represents a part of a whole. It consists of two numbers: the numerator (the top number) and the denominator (the bottom number). The numerator indicates how many parts we have, while the denominator indicates how many equal parts the whole is divided into. For example, in the fraction 1/6, 1 is the numerator and 6 is the denominator. This means we are considering one out of six equal parts.

Key Concepts:

• Numerator: The top number, representing the number of parts.
• Denominator: The bottom number, representing the total number of equal parts.
• Proper Fraction: A fraction where the numerator is less than the denominator (e.g., 1/6, 3/4).
• Improper Fraction: A fraction where the numerator is greater than or equal to the denominator (e.g., 7/4, 5/5).
• Mixed Number: A number consisting of a whole number and a proper fraction (e.g., 1 3/4).

Calculating 1/6 of 48: Method 1 - Direct Multiplication

The most straightforward method to find 1/6 of 48 is through direct multiplication. We can express "of" as multiplication, transforming the problem into a multiplication of fractions:

(1/6) * 48

To perform this calculation, we can rewrite 48 as a fraction with a denominator of 1:

(1/6) * (48/1)

Now, we multiply the numerators together and the denominators together:

(1 * 48) / (6 * 1) = 48/6

Finally, we simplify the fraction by dividing the numerator by the denominator:

48 ÷ 6 = 8

Therefore, 1/6 of 48 is 8.

Calculating 1/6 of 48: Method 2 - Division First

An alternative approach involves dividing 48 by the denominator (6) first, then multiplying the result by the numerator (1). This method emphasizes the concept of dividing the whole into equal parts before selecting a specific number of parts.

First, divide 48 by 6:

48 ÷ 6 = 8

This tells us that each of the six equal parts of 48 is 8. Since we want 1/6, we take one of these parts:

8 * 1 = 8

Again, we arrive at the answer: 1/6 of 48 is 8.

Real-World Applications

Understanding how to calculate fractions is crucial in various real-world scenarios. Here are a few examples:

• Sharing Resources: Imagine you have 48 cookies to share equally among 6 friends. Finding 1/6 of 48 tells you how many cookies each friend receives (8 cookies).
• Cooking and Baking: Many recipes involve fractions. If a recipe calls for 1/6 of a cup of sugar, and you need to double the recipe, you'll need to calculate 1/6 of a cup twice.
• Discounts and Sales: Stores often offer discounts as fractions (e.g., 1/3 off). Calculating 1/6 of the original price helps determine the amount of discount.
• Financial Calculations: Fractions are used extensively in finance, for example, calculating interest rates, determining portions of investments, or calculating portions of profits or losses.

Expanding the Concept: Finding Other Fractions of 48

The methods described above can be easily adapted to calculate other fractions of 48. For example, let's find 2/6 of 48:

Method 1 (Direct Multiplication):

(2/6) * (48/1) = (2 * 48) / (6 * 1) = 96/6 = 16

Method 2 (Division First):

48 ÷ 6 = 8 (one-sixth of 48) 8 * 2 = 16 (two-sixths of 48)

Similarly, you can find 3/6, 4/6, 5/6, or any other fraction of 48 using these methods.

Simplifying Fractions

Notice that in the example of finding 2/6 of 48, the resulting fraction 96/6 can be simplified. Simplifying a fraction means reducing it to its lowest terms. To simplify a fraction, we find the greatest common divisor (GCD) of the numerator and denominator, and divide both by it.

In the case of 96/6, the GCD is 6. Dividing both the numerator and the denominator by 6 gives us:

96/6 = 16/1 = 16

Simplifying fractions makes calculations easier and presents the answer in its most concise form.

Converting Improper Fractions to Mixed Numbers

Sometimes, the result of a fraction calculation might be an improper fraction. For example, if we were to calculate 7/6 of 48, we would get:

(7/6) * 48 = 336/6 = 56

While this is correct, it's often more convenient to express this as a mixed number. To convert an improper fraction to a mixed number, we divide the numerator by the denominator. The quotient becomes the whole number part, and the remainder becomes the numerator of the fractional part. The denominator remains the same.

In the case of 56/6:

56 ÷ 6 = 9 with a remainder of 2

Therefore, 56/6 is equivalent to 9 2/6, which can be further simplified to 9 1/3.

Conclusion: Mastering Fractions

This comprehensive guide demonstrates various approaches to solving the problem "What is 1/6 of 48?". By understanding the fundamental principles of fractions, including multiplication, division, simplification, and conversion between improper fractions and mixed numbers, you can confidently tackle similar problems and apply these concepts in various real-world situations. Remember to practice regularly to solidify your understanding and build proficiency in working with fractions. This will not only improve your mathematical skills but also your problem-solving abilities across different domains. The ability to quickly and accurately calculate fractions is a valuable asset in many fields, from accounting and finance to engineering and cooking. Mastering this fundamental skill empowers you to approach more complex mathematical concepts with greater confidence and ease.