Understanding Fraction Addition in Cake Consumption: A Practical Guide

Have you ever wondered how much cake you have left when you divide it into fractions and eat them at different times? This article will walk you through a practical example, using fraction addition to solve the problem of how much cake remains.

Step-by-Step Solution to the Cake Consumption Problem

Let's consider the scenario where you eat a quarter of a cake first and then consume two-thirds of the same cake later. The key to solving this problem is to add the fractions appropriately, ensuring they share a common denominator.

Step 1: Convert the Fractions to a Common Denominator

The denominators of the fractions are 4 and 3. The least common multiple (LCM) of 4 and 3 is 12. We need to convert both fractions so they share this common denominator.

Convert 1/4 to 3/12:

4 is the denominator, and we need to multiply it by 3 to get 12. Therefore, we also multiply the numerator by 3.

1/4 1 × 3 / 4 × 3 3/12

Convert 2/3 to 8/12:

3 is the denominator, and we need to multiply it by 4 to get 12. Therefore, we also multiply the numerator by 4.

2/3 2 × 4 / 3 × 4 8/12

Step 2: Add the Fractions

Now that both fractions share a common denominator, we can add them.

3/12 8/12 11/12

Step 3: Calculate the Remaining Cake

We started with a whole cake, which represents 12/12. To find out how much cake is left, subtract the consumed fraction from the whole:

12/12 - 11/12 1/12

Thus, you have 1/12 of the cake left, which is approximately 8.33% of the original cake.

Application in Other Scenarios

Let's consider another example for clarity:

Additional Example

Suppose you eat 2/5 of a cake, and then 1/2x of the remaining cake.

Calculate the remaining cake after eating 2/5:

1 - 2/5 3/5

Convert 1/2x to a fraction:

Determine the least common multiple (LCM) of 2 and 5, which is 10.

1/2 × 5/5 5/10

Subtract the fraction from the remaining cake:

(3/5) - (5/10) 3/5 - 1/2 6/10 - 5/10 1/10

In this scenario, 1/10 of the cake remains.

Three Fifths of the Half-Cake

An even simpler example involves fractions of another fractional part of the cake. If you take 3/5 of the remaining half-cake, you are essentially dealing with a fraction of a fraction.

3/5 of 1/2 3/5 × 1/2 3/(5 × 2) 3/10

So, you have 3/10 of the original cake left.

Conclusion

Understanding how to add fractions, especially when dealing with real-life situations like cake consumption, is a valuable skill. Whether you are doing it manually or using a calculator, the key is to ensure the fractions have a common denominator before performing the addition.

Remember, the fraction of the cake you have left can be less or more than you initially thought, depending on the fractions involved and the order in which they are consumed.

Enjoy your remaining cake!