A school girl spends $\frac{1}{4}$ of her pocket money on books and $\frac{1}{3}$ on dress. What fraction remains?

Analysis

To find the remaining fraction of the pocket money, we need to calculate the total fraction spent and subtract that value from the whole (which is represented as 1).

Concept

When dealing with fractions of a whole, the total amount is always represented by $1$. If you spend parts of that whole, you subtract the sum of the spent parts from $1$ to find what is left.

Step-by-Step Solution

Step 1: Calculate the total fraction spent. The girl spent $\frac{1}{4}$ on books and $\frac{1}{3}$ on dress. To add these, we find the Least Common Multiple (LCM) of the denominators (4 and 3), which is 12.

Convert the fractions to have a denominator of 12:

Step 2: Calculate the remaining fraction. Subtract the total spent from the whole (1):

Represent 1 as a fraction with the same denominator:

Conclusion

The fraction of the pocket money that remains is $\frac{5}{12}$. This matches option C.

Exam Tip

When adding or subtracting fractions, always look for the LCM of the denominators first. If you are ever unsure about your fraction arithmetic, imagine the pocket money as a specific amount (like ₦120).

• $\frac{1}{4}$ of 120 = ₦30
• $\frac{1}{3}$ of 120 = ₦40
• Total spent = ₦70
• Remaining = 120 - 70 = ₦50
• Fraction remaining = $\frac{50}{120} = \frac{5}{12}$. Using a "dummy" number like this is a great way to double-check your work during the exam!