Jagya cleaned `1/(7)` of the school playground while his friends Bashir and Hazel cleaned `2/(7) and 3/(7)` of the playground, respectively. How much did they clean together? What portion of the playground is yet to be cleaned?

Answer

To solve the problem step by step, we will first calculate how much of the playground Jagya, Bashir, and Hazel cleaned together, and then determine what portion of the playground is yet to be cleaned.

### Step 1: Identify the fractions cleaned by each person
- Jagya cleaned \( \frac{1}{7} \) of the playground.
- Bashir cleaned \( \frac{2}{7} \) of the playground.
- Hazel cleaned \( \frac{3}{7} \) of the playground.

### Step 2: Add the fractions together
To find the total area cleaned by all three, we add their fractions:
\[ \text{Total cleaned} = \frac{1}{7} + \frac{2}{7} + \frac{3}{7} \]

Since the denominators are the same (7), we can add the numerators directly:
\[ \text{Total cleaned} = \frac{1 + 2 + 3}{7} = \frac{6}{7} \]

### Step 3: Calculate the portion yet to be cleaned
The whole playground is considered as 1 (or \( \frac{7}{7} \)). To find out how much is left to clean, we subtract the total cleaned from the whole:
\[ \text{Portion yet to be cleaned} = 1 - \frac{6}{7} \]

To perform the subtraction, we convert 1 into a fraction with a denominator of 7:
\[ 1 = \frac{7}{7} \]
Now we can subtract:
\[ \text{Portion yet to be cleaned} = \frac{7}{7} - \frac{6}{7} = \frac{1}{7} \]

### Final Answer
- Together, Jagya, Bashir, and Hazel cleaned \( \frac{6}{7} \) of the playground.
- The portion of the playground that is yet to be cleaned is \( \frac{1}{7} \).

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