Calculating Remaining Pocket Money: A Simple Math Problem

Have you ever wondered how to solve a problem involving the remaining amount of pocket money when expenditures are made on different days? This article aims to clarify the process by breaking down a specific scenario. Let's explore the steps in detail, ensuring that you understand how to handle such problems effectively.

Solving the Problem

Imagine a person who spends 1/4 of their pocket money on Monday and 3/8 on Wednesday. The task is to determine what fraction of their money remains. The key to solving this problem lies in making the fractions have a common denominator.

Step 1: Making Denominators Identical

Firstly, we make the denominators of the fractions the same. The denominators here are 4 and 8. The least common multiple (LCM) of 4 and 8 is 8.

Converting 1/4 to a Fraction with a Denominator of 8

Since 4 × 2 8, we multiply both the numerator and the denominator of 1/4 by 2:

[[frac{1}{4} frac{1 times 2}{4 times 2} frac{2}{8}]]

Step 2: Adding the Fractions

Now, we add the fractions with the common denominator:

[[frac{2}{8} frac{3}{8} frac{2 3}{8} frac{5}{8}]]

This means the person has spent 5/8 of their pocket money. To find the remaining fraction, we subtract 5/8 from 1 (which represents the whole amount).

Step 3: Calculating the Remaining Fraction

The whole can be considered as 1, which is 8/8. Therefore:

[[1 - frac{5}{8} frac{8}{8} - frac{5}{8} frac{3}{8}]]

Conclusion

Thus, the fraction of the person's money that remains is 3/8. This method can be applied to similar problems where expenditures are made on different days with different fractions.

Exploring More Scenarios

Now, let’s explore a couple more scenarios to further solidify our understanding:

Scenario 2: 1/32 and 5/32 of the Money

Suppose the person spends 1/3 of their pocket money on one day and 5/6 on another. First, we convert 1/3 to a fraction with a denominator of 18 (since 3 × 6 18):

[[frac{1}{3} frac{1 times 6}{3 times 6} frac{6}{18}]]

Now, we add the fractions:

[[frac{6}{18} frac{5}{18} frac{11}{18}]]

The remaining fraction is:

[[1 - frac{11}{18} frac{18}{18} - frac{11}{18} frac{7}{18}]]

Scenario 3: 1/4 and 1/2 of the Money

For the last scenario, if the person spends 1/4 on Monday and 1/2 on Tuesday:

Convert 1/2 to a fraction with a denominator of 4 (since 2 × 2 4):

[[frac{1}{2} frac{1 times 2}{2 times 2} frac{2}{4}]]

Add the fractions:

[[frac{1}{4} frac{2}{4} frac{1 2}{4} frac{3}{4}]]

The remaining fraction is:

[[1 - frac{3}{4} frac{4}{4} - frac{3}{4} frac{1}{4}]]

Through these scenarios, we have seen how to approach and solve problems involving the remaining fraction of pocket money. Understanding the method clearly and systematically will surely aid in tackling similar mathematical problems.

Conclusion

By mastering the steps of finding a common denominator, adding fractions, and subtracting them from the whole, you can efficiently determine the remaining fraction of pocket money after expenditures. This skill is not only useful for math problems but can also be applied in various real-life situations.