To find the fractional part of Ms. Bhagya's earnings that she has left after spending on food, rent, and other expenses, we need to follow these steps:

1. Sum up the fractional parts spent:

   • Food: $\frac{3}{16}$
   • Rent: $\frac{5}{18}$
   • Other expenses: $\frac{7}{12}$

   We first need to find the sum of these fractions. To do this, we need a common denominator. The least common denominator (LCD) of 16, 18, and 12 is 144.

   Now, let's convert each fraction to have a denominator of 144: $\frac{3}{16} = \frac{3 \times 9}{16 \times 9} = \frac{27}{144}$ $\frac{5}{18} = \frac{5 \times 8}{18 \times 8} = \frac{40}{144}$ $\frac{7}{12} = \frac{7 \times 12}{12 \times 12} = \frac{84}{144}$

2. Add the fractions together: $\frac{27}{144} + \frac{40}{144} + \frac{84}{144} = \frac{27 + 40 + 84}{144} = \frac{151}{144}$

   So, the total fraction spent is $\frac{151}{144}$.

3. Find the fractional part left:

   Ms. Bhagya had the whole of her earnings initially, which is represented by $1$. The fractional part left is: $1 - \frac{151}{144} = \frac{144}{144} - \frac{151}{144} = \frac{144 - 151}{144} = \frac{-7}{144}$

   Since the result is negative, it means she spent more than her earnings by $\frac{7}{144}$.

So, Ms. Bhagya has overspent her earnings by $\frac{7}{144}$.

Would you like further details on this, or have any questions?

Here are 5 related questions to think about:

1. How do you determine the least common denominator of fractions?
2. What happens when your expenses exceed your earnings in real life?
3. How do you subtract fractions with different denominators?
4. How could you adjust your budget to avoid overspending?
5. How do you simplify fractions after performing arithmetic on them?

Tip: When dealing with fractions, always make sure they have a common denominator before adding or subtracting them.