Understanding Fractions with a Mathematical Cake Problem

This article explains step-by-step how to solve a mathematical problem involving fractions by using the example of a cake divided among several people. By following this detailed guide, you'll understand the calculation of remaining portions and the importance of common denominators in fraction arithmetic.

Solving the Problem

Imagine Tom baked a cake and we need to determine how much cake is left after several people take their shares. Let's break down the problem step by step.

Sam takes his share

First, Sam eats 1/6 of the cake.Total cake: 1Sam's share: 1/6Remaining cake: 1 - 1/6 5/6

Brooke takes her share

Then, Brooke takes 1/5 of the remaining cake.Total remaining cake: 5/6Brooke's share: 1/5 * 5/6 1/6Remaining cake: 5/6 - 1/6 4/6 2/3

Hashir takes his share

After Brooke, Hashir takes 1/4 of the remaining cake.Total remaining cake: 2/3Hashir's share: 1/4 * 2/3 1/6Remaining cake: 2/3 - 1/6 4/6 - 1/6 3/6 1/2

Ben takes his share

Finally, Ben takes 1/2 of the remaining cake.Total remaining cake: 1/2Ben's share: 1/2 * 1/2 1/4Remaining cake: 1/2 - 1/4 2/4 - 1/4 1/4

Conclusion

The final amount of cake left after everyone has taken their shares is 1/4 of the original cake.

Alternative Method Using Lowest Common Denominator

An alternative method involves working with the lowest common denominator, which is 60.

Starting with 60 slices of cake:Sam eats 1/6 of 60 slices, leaving 50 eats 1/5 of the remaining 50 slices, leaving 40 slices.Hashir eats 1/4 of the remaining 40 slices, leaving 30 eats 1/2 of the remaining 30 slices, leaving 15 , 15/60 or 1/4 of the cake remains.

Original Cake Distribution

For a clearer understanding, let's track the distribution of cake slices step by step:Sam: 6/6 - 1/6 5/6Brooke: 5/6 * 5/6 25/36 (simplified 25/30 - 6/30 19/30)Hashir: 19/30 * 3/4 57/120 (simplified to 38/60 - 15/60 23/60)Ben: 23/60 * 1/2 23/120 (simplified to 46/120 - 23/120 23/120)Remaining: 120/120 - 23/120 97/120, simplifying to 1/4

Thus, the final amount of cake left is 1/4.