Kumud brought `70/(3)` metres of ribbon of which she used `71/(4)` metres in a dress. Find the length of ribbon left with Kumud.

Answer

To find the length of ribbon left with Kumud after using some for a dress, we can follow these steps:

### Step 1: Identify the total length of ribbon and the length used
Kumud bought a total of \( \frac{70}{3} \) meters of ribbon and used \( \frac{71}{4} \) meters for a dress.

### Step 2: Set up the equation for the remaining ribbon
The length of ribbon left can be calculated by subtracting the length used from the total length:
\[ \text{Length left} = \text{Total length} - \text{Length used} \]
\[ \text{Length left} = \frac{70}{3} - \frac{71}{4} \]

### Step 3: Find the least common multiple (LCM) of the denominators
The denominators are 3 and 4. The LCM of 3 and 4 is 12.

### Step 4: Convert the fractions to have a common denominator
We need to convert both fractions to have the common denominator of 12:
- For \( \frac{70}{3} \):
\[ \frac{70}{3} = \frac{70 \times 4}{3 \times 4} = \frac{280}{12} \]
- For \( \frac{71}{4} \):
\[ \frac{71}{4} = \frac{71 \times 3}{4 \times 3} = \frac{213}{12} \]

### Step 5: Subtract the two fractions
Now we can subtract the two fractions:
\[ \text{Length left} = \frac{280}{12} - \frac{213}{12} = \frac{280 - 213}{12} = \frac{67}{12} \]

### Step 6: Convert the improper fraction to a mixed number (if needed)
To convert \( \frac{67}{12} \) to a mixed number:
- Divide 67 by 12. The quotient is 5 and the remainder is 7.
\[ \frac{67}{12} = 5 \frac{7}{12} \]

### Final Answer
The length of ribbon left with Kumud is \( \frac{67}{12} \) meters or \( 5 \frac{7}{12} \) meters.

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