Calculating the Number of Sandwiches Sold

Oct 13, 2025 by vinooalluri.com 82 views

Introduction

In the world of mathematics, problems often arise in the most unexpected places. A canteen with 72 sandwiches, for instance, presents a simple yet intriguing scenario. If the canteen sold 5/6 of its sandwiches, how many were sold? In this article, we will delve into the world of fractions and proportions to uncover the answer.

Understanding Fractions

Fractions are a fundamental concept in mathematics, representing a part of a whole. In this case, the canteen sold 5/6 of its sandwiches. To understand this, let's break down the fraction 5/6.

The top number, 5, represents the number of parts sold.
The bottom number, 6, represents the total number of parts.

Calculating the Number of Sandwiches Sold

To find the number of sandwiches sold, we need to multiply the fraction 5/6 by the total number of sandwiches, which is 72.

(5/6) × 72 = ?

To solve this, we can multiply the numerator (5) by the total number of sandwiches (72) and then divide by the denominator (6).

(5 × 72) ÷ 6 = ?

First, let's calculate the numerator:

5 × 72 = 360

Now, let's divide the result by the denominator:

360 ÷ 6 = 60

Conclusion

Therefore, the canteen sold 60 sandwiches, which is 5/6 of the total number of sandwiches available.

Real-World Applications

This problem may seem trivial, but it has real-world implications. In a business setting, understanding fractions and proportions can help with inventory management, sales forecasting, and resource allocation. By applying mathematical concepts to everyday problems, we can make informed decisions and optimize our operations.

Additional Examples

To further illustrate the concept, let's consider a few more examples:

If a bakery has 24 cakes and sells 3/4 of them, how many cakes were sold?
If a store has 48 shirts and sells 2/3 of them, how many shirts were sold?

In both cases, we can apply the same mathematical concept to find the answer.

Solving the First Example

Let's solve the first example:

Total number of cakes: 24
Fraction sold: 3/4

To find the number of cakes sold, we can multiply the fraction 3/4 by the total number of cakes:

(3/4) × 24 = ?

To solve this, we can multiply the numerator (3) by the total number of cakes (24) and then divide by the denominator (4).

(3 × 24) ÷ 4 = ?

First, let's calculate the numerator:

3 × 24 = 72

Now, let's divide the result by the denominator:

72 ÷ 4 = 18

Solving the Second Example

Let's solve the second example:

Total number of shirts: 48
Fraction sold: 2/3

To find the number of shirts sold, we can multiply the fraction 2/3 by the total number of shirts:

(2/3) × 48 = ?

To solve this, we can multiply the numerator (2) by the total number of shirts (48) and then divide by the denominator (3).

(2 × 48) ÷ 3 = ?

First, let's calculate the numerator:

2 × 48 = 96

Now, let's divide the result by the denominator:

96 ÷ 3 = 32

Conclusion

In conclusion, understanding fractions and proportions is essential in mathematics and has real-world applications. By applying mathematical concepts to everyday problems, we can make informed decisions and optimize our operations. The examples provided in this article demonstrate how to solve problems involving fractions and proportions, and we can apply these concepts to a wide range of scenarios.

Final Thoughts

Mathematics is all around us, and it's essential to understand its concepts to navigate the world effectively. By mastering fractions and proportions, we can solve problems, make informed decisions, and optimize our operations. Whether it's a canteen selling sandwiches or a business managing inventory, mathematics plays a crucial role in our daily lives.