Calculating Rotten Oranges: An In-Depth Look

Introduction to the Problem

The question at hand is: if there are 46 oranges in a box and 1 in every 6 oranges is rotten, how many rotten oranges are there in total?

Method 1: Using Total Multiplication and Proportion

First, let’s find the total number of oranges. Assuming there are 5 boxes, each containing 48 oranges, the calculation would be:

5 boxes × 48 oranges per box 240 oranges

To find the number of rotten oranges, we know that 1 in every 6 oranges is rotten. So, the calculation would be:

240 oranges × (1/6) 40/6 ≈ 40/6 12 rotten oranges

Method 2: Simplified Calculation Using Percentages

A more straightforward method is to use percentages:

5 out of 100 is equivalent to 5%, so the calculation is:

240 oranges × 5% 240 × 0.05 12 rotten oranges

Alternatively, we can represent 5% as a fraction and a decimal:

5/100 or 0.05, which simplifies our calculation process.

Method 3: Using Mental Arithmetic and Fractions

Another approach involves using fractions:

20 is a twentieth of 40, leaving a remainder of 8. Thus:

48 ÷ 20 2 remainder 8, which is expressed as 2 and 8/20 or 2 and 4/10 or 2.4

Multiplying this by 5 (the number of fifths in 1/6) gives:

5 × 4.8 24, and 24/6 4 rotten oranges. But to find 5/100, we perform:

5 × 48 ÷ 20 12 rotten oranges

Alternative Scenario: Different Box Quantities

In an alternative scenario, if each box contains 48 oranges in a total of 5 boxes, and if we assume the closest whole number to 46/6 is 8, then:

5 boxes × (1/6) of 48 oranges 8 rotten oranges

This method requires rounding to the nearest whole number due to a lack of perfect divisibility.

Conclusion

Through these methods, we can accurately calculate the number of rotten oranges in a given scenario. Whether through simple multiplication, percentages, or mental arithmetic, the key is to understand the proportional relationship and apply it correctly.