Solving Cake Sharing Problems: Fractions and How to Compute Uneaten Portions

Sharing a cake with friends or family can be a delightful experience, but it often involves some math! This guide will help you understand how to solve problems where different people eat different portions of cake and how to determine the remaining uneaten fraction. We'll walk through the process with practical examples and provide resources like fraction calculators that can assist you.

Example 1: Ali and Jason Share a Cake

Let's start with a simple problem: Ali ate 1/3 of a cake and Jason ate 1/4 of it. To find out what fraction of the cake was still uneaten, we need to subtract the fractions that Ali and Jason ate from the whole cake.

Step-by-Step Solution

First, identify the fractions each person ate:

Ali ate 1/3 of the cake. Jason ate 1/4 of the cake.

Find a common denominator for the fractions. The least common multiple of 3 and 4 is 12, so we will convert both fractions to have a denominator of 12:

Ali's fraction: 1/3 4/12 (multiply numerator and denominator by 4) Jason's fraction: 1/4 3/12 (multiply numerator and denominator by 3)

Now, subtract the fractions:

4/12 - 3/12 1/12

Therefore, 1/12 of the cake was still uneaten.

Example 2: Converting and Subtracting Fractions

In another scenario, we have two slices with different denominators. To find out how much of the cake is uneaten, we need to make the fractions equivalent by converting them to have a common denominator.

Convert 1/3 to 12ths by multiplying numerator and denominator by 4:

1/3 4/12

Convert 1/4 to 12ths by multiplying numerator and denominator by 3:

1/4 3/12

Add the two fractions together to see how much of the cake was eaten:

4/12 3/12 7/12

Subtract 7/12 from the whole cake (12/12) to find the uneaten portion:

12/12 - 7/12 5/12

The decimal equivalent is 0.416666…

Additional Problem

In this case, Nobita ate 5/12 of the cake, and Doraemon ate 1.3 (or 13/10) of Dora's cake. To find out the remaining fraction of the cake, follow these steps:

Calculation

Let y the fraction of cake remaining after 5/12 and 13/10 have been eaten:

y 1 - (5/12 13/10)

Add the two fractions to determine the total eaten:

5/12 13/10 (5*10 13*12) / (12*10) 50 156 / 120 206 / 120

Subtract this total from 1 (or 120/120) to find the remaining portion:

y 120/120 - 206/120 -86/120

Since the fraction -86/120 is negative, it indicates that the total eaten exceeds the whole cake. Therefore, no cake is left uneaten.

Fraction Calculator

When dealing with such problems, a fraction calculator can be incredibly useful. Here are a couple of resources you can use:

Fraction Calculator - Example 1: 1 - 1/3 - 1/4 5/12

Fraction Calculator - Example 2: 1 - 1/3 - 1/4 5/12

General Fraction Calculator: Enter the fractions directly into the calculator to find the remainder.

These calculators can help you save time and ensure accuracy. By following the steps provided in this guide and using these tools, you can solve many fraction-related problems involving cake sharing or other similar scenarios.