Understanding Fractions Through a Cake-Eating Scenario

Let's explore a real-world example to better understand fractions through a simple story involving Mavis, her brother, and a birthday cake. This example will help us visualize and calculate fractions, helping us understand why a certain fraction is missing to make the cake whole.

Mavis Ate 3/10 of Her Birthday Cake and Her Brother Ate 1/4 of It

Mavis ate a part of the cake, specifically 3/10 of it. To understand this better, we can convert this fraction into a common denominator.

Step 1: Converting 3/10 to a Common Denominator

[3/10 6/20]

Step 2: Converting 1/4 to a Common Denominator

Her brother ate 1/4 of the cake. Converting this to a common denominator of 20:

[1/4 5/20]

Step 3: Combining the Portions Eaten

Now, we add both portions to know the total fraction of the cake that was eaten.

[6/20 5/20 11/20]

This means that 11/20 of the cake has been eaten by Mavis and her brother together.

Step 4: Calculating the Missing Portion

Since the whole cake is 1 (or 20/20), we can find the missing portion by subtracting the eaten portion from the whole cake.

[20/20 - 11/20 9/20]

So, the fraction of the cake that is missing to make it whole is 9/20.

Visualizing the Fractions

Through the use of fractions, we can represent the situation with a visual model. If we imagine the cake is divided into 20 equal parts, Mavis ate 6 parts and her brother ate 5 parts, totaling 11 parts.

Out of these 20 parts, 11 are eaten, and therefore 9 parts remain.

Conclusion

By breaking down the problem and visualizing the fractions, we understood that the fraction of the cake that was bought and is missing to make the cake whole is 9/20.

Through this example, we see how fractions can be used to describe everyday scenarios, making it easier to understand and solve similar problems.

Key Takeaways

1/1 of the cake was initially bought. [3/10 1/4 11/20] of the cake is missing or eaten. [20/20 - 11/20 9/20] is the fraction of the cake that is left.

These steps and calculations not only help in solving the problem but also in providing a deeper understanding of fractions and their application in real-life situations.