Diksha earned some money. She spent `1/3` of the money on vegetables and `1/4` of the money on a dress. Which of the following fractions represents the part of money left with her?

Options

A. `5/12`
B. `1/2`
C. `2/3`
D. `5/7`

Answer

To find the part of money left with Diksha after her expenditures, we can follow these steps:

### Step 1: Identify the fractions spent
Diksha spent:
- \( \frac{1}{3} \) of her money on vegetables
- \( \frac{1}{4} \) of her money on a dress

### Step 2: Find a common denominator
To add the fractions \( \frac{1}{3} \) and \( \frac{1}{4} \), we need to find a common denominator. The least common multiple (LCM) of 3 and 4 is 12.

### Step 3: Convert the fractions
Convert \( \frac{1}{3} \) and \( \frac{1}{4} \) to have a denominator of 12:
- \( \frac{1}{3} = \frac{4}{12} \) (since \( 1 \times 4 = 4 \) and \( 3 \times 4 = 12 \))
- \( \frac{1}{4} = \frac{3}{12} \) (since \( 1 \times 3 = 3 \) and \( 4 \times 3 = 12 \))

### Step 4: Add the fractions
Now, add the two fractions:
\[ \frac{4}{12} + \frac{3}{12} = \frac{4 + 3}{12} = \frac{7}{12} \]

### Step 5: Calculate the part of money left
The total fraction of money spent is \( \frac{7}{12} \). To find the part of money left, subtract the spent fraction from 1 (which represents the whole):
\[ 1 - \frac{7}{12} = \frac{12}{12} - \frac{7}{12} = \frac{5}{12} \]

### Final Answer
The part of money left with Diksha is \( \frac{5}{12} \).

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