Calculating the Fraction of Red Balls in a Box

In everyday life, it is quite common to deal with scenarios involving probability and fractions. Let's consider a scenario with a box containing 40 balls, where 15 of these balls are blue, and the rest are red. Our task is to find the fraction of balls that are red.

Step-by-Step Solution

First, we determine the number of red balls. Given that there are a total of 40 balls and 15 of them are blue, we can deduce the number of red balls by subtracting the number of blue balls from the total number of balls:

Step 1: Calculate the Number of Red Balls

The number of red balls:

[text{Number of red balls} text{Total balls} - text{Blue balls} 40 - 15 25]

Step 2: Determine the Fraction of Red Balls

Next, we express the fraction of balls that are red by dividing the number of red balls by the total number of balls:

[text{Fraction of red balls} frac{text{Number of red balls}}{text{Total balls}} frac{25}{40}]

Step 3: Simplify the Fraction

The fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 5:

[frac{25 div 5}{40 div 5} frac{5}{8}]

Hence, the fraction of balls that are red is (frac{5}{8}).

Further Insights

In addition to the fraction, it can be interesting to explore the probability and percentage representation of the solution.

Probability of Drawing a Red Ball

The probability of drawing a red ball is the number of red balls divided by the total number of balls, which we have already calculated as (frac{25}{40}). Simplifying this further yields (frac{5}{8}).

Percentage Representation

To convert the fraction to a percentage, we multiply the fraction by 100:

[frac{25}{40} times 100 62.5%]

Thus, 62.5% of the balls in the box are red.

Conclusion

This simple calculation demonstrates how we can systematically approach and solve problems involving fractions and probability. Understanding these fundamental concepts is crucial in various fields, including statistics, data science, and everyday applications.