What is 48 Divided by 6/7?

Dividing a whole number by a fraction, such as 48 divided by 6/7, is a mathematical operation that involves understanding the principles of division and working with fractions. In this comprehensive blog post, we will explore the concept of dividing by a fraction, discuss the step-by-step process for calculating 48 divided by 6/7, explain the importance of this calculation, and provide practical examples of when it is relevant.

What is 48 Divided by 6/7?

To divide 48 by 6/7, you multiply 48 by the reciprocal of 6/7, which is 7/6. The result is 48 multiplied by 7/6, which equals 56. So, 48 divided by 6/7 equals 56.

Understanding Division by a Fraction

When you divide a whole number by a fraction, you are essentially asking how many times the fraction can fit into the whole number. It’s important to remember that division by a fraction is the same as multiplying by its reciprocal (the fraction flipped upside down). In this case, dividing 48 by 6/7 is the same as multiplying 48 by 7/6.

Calculating 48 Divided by 6/7

To calculate 48 divided by 6/7, follow these steps:

1. Convert the Division to Multiplication:

• Instead of dividing by 6/7, you can multiply by its reciprocal, which is 7/6. This step simplifies the calculation: 48 × (7/6).

2. Perform the Multiplication:

• Multiply the whole number (48) by the fraction (7/6).
• To multiply a whole number by a fraction, you can first write the whole number as a fraction by placing it over 1: 48/1.
• Now, multiply the fractions by multiplying the numerators (top numbers) together and the denominators (bottom numbers) together:(48/1) × (7/6) = (48 × 7) / (1 × 6) = 336/6.

3. Simplify the Result:

• To simplify the fraction further, you can find the greatest common factor (GCF) of the numerator and denominator, which in this case is 6.
• Divide both the numerator and denominator by the GCF (6) to simplify the fraction:(336/6) ÷ (6/6) = 56/1.

4. Express as a Whole Number:

• The simplified fraction 56/1 can be expressed as a whole number, which is simply 56.

The Importance of Division by a Fraction

Understanding how to divide by a fraction is important in various real-life scenarios:

1. Cooking and Recipes:

• When adjusting recipes, you may need to divide or multiply ingredients by fractions to achieve the desired serving size.

2. Construction and Measurements:

• In construction, when dividing lengths or quantities, it’s crucial to work with fractions for precision.

3. Financial Transactions:

• In finance, dividing by fractions is important for calculating interest rates, investments, and financial ratios.

4. Educational Context:

• Understanding division by fractions is fundamental in mathematics education and problem-solving.

Practical Examples

Let’s explore practical scenarios where division by a fraction is relevant:

1. Recipe Scaling:

• If a recipe serves 6 people, and you want to make it for 7 people, you need to divide the ingredient quantities by the fraction 6/7.

2. Construction:

• When dividing a length of wood into equal parts for shelving, you may need to divide it by a fraction to ensure the shelves fit precisely.

3. Financial Investments:

• When calculating the return on investment (ROI) for a business project, you may need to divide the project’s net profit by the initial investment, which could involve fractions.

4. Educational Exercises:

• In math classes and textbooks, students encounter division by fractions as they learn to work with fractions and decimals.

Conclusion

Dividing a whole number by a fraction, as demonstrated in the calculation of 48 divided by 6/7, is a fundamental mathematical operation with practical applications in various fields. Understanding the concept of division by a fraction, converting it to multiplication by the reciprocal, and simplifying the result are valuable skills for solving problems, making accurate measurements, and ensuring proportional distribution of quantities. Division by fractions is a foundational concept in mathematics that serves as a building block for more advanced mathematical and practical calculations.