Ms. Bhagya spent 3/16 of her monthly earnings for food, 5/18 for rent, and 7/12 for other expenses. Find the fractional part left of her earnings.

To find the fractional part of Ms. Bhagya's earnings that she has left, we need to first determine the total fraction of her earnings spent and subtract that from 1 (the whole of her earnings).

The fractions she spent are:

- For food: \( \frac{3}{16} \)
- For rent: \( \frac{5}{18} \)
- For other expenses: \( \frac{7}{12} \)

First, we will find the total amount spent by adding these fractions.

### Step 1: Find a common denominator
The denominators are 16, 18, and 12. The least common denominator (LCD) of 16, 18, and 12 is 144.

### Step 2: Convert the fractions to have a denominator of 144
- \( \frac{3}{16} = \frac{3 \times 9}{16 \times 9} = \frac{27}{144} \)
- \( \frac{5}{18} = \frac{5 \times 8}{18 \times 8} = \frac{40}{144} \)
- \( \frac{7}{12} = \frac{7 \times 12}{12 \times 12} = \frac{84}{144} \)

### Step 3: Add the fractions
Now, add the fractions:
\[
\frac{27}{144} + \frac{40}{144} + \frac{84}{144} = \frac{27 + 40 + 84}{144} = \frac{151}{144}
\]

### Step 4: Find the fractional part left
Since Ms. Bhagya cannot spend more than her earnings, the fraction left of her earnings is:
\[
1 - \frac{151}{144} = \frac{144}{144} - \frac{151}{144} = \frac{-7}{144}
\]

Since this is a negative number, it means she has overspent by \( \frac{7}{144} \) of her monthly earnings.

Thus, Ms. Bhagya has overspent by \( \frac{7}{144} \), or approximately 0.0486 of her monthly earnings.

Do you have any further questions, or would you like a detailed explanation on a specific part of the process?

Here are 5 related questions to think about:
1. What is the least common denominator of three different fractions?
2. How do you handle situations where spending exceeds earnings in real life?
3. Can you simplify the fraction \( \frac{7}{144} \)?
4. How do we convert improper fractions into mixed numbers?
5. What are some strategies to avoid overspending in personal budgeting?

**Tip:** When adding fractions, finding the least common denominator (LCD) makes the process much easier and faster.

Learn how to calculate the fractional part left of Ms. Bhagya’s earnings after spending fractions of her income on food, rent, and other expenses. This detailed step-by-step guide covers fraction addition and subtraction, suitable for students in Grades 6-8.

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