Simplify the following :
`(3/7+1/2) div 7/8`

Answer

To simplify the expression \((\frac{3}{7} + \frac{1}{2}) \div \frac{7}{8}\), we will follow these steps:

### Step 1: Solve the expression inside the parentheses
We need to add \(\frac{3}{7}\) and \(\frac{1}{2}\). Since the denominators are different, we will find the least common multiple (LCM) of 7 and 2.

**Hint:** The LCM of two numbers is the smallest number that both can divide without leaving a remainder.

### Step 2: Find the LCM of 7 and 2
The LCM of 7 and 2 is \(14\).

**Hint:** To find the LCM, you can multiply the two numbers if they have no common factors, as is the case here.

### Step 3: Convert each fraction to have the same denominator
Now, we convert both fractions to have the denominator of 14:
- For \(\frac{3}{7}\), multiply the numerator and denominator by 2:
\[ \frac{3 \times 2}{7 \times 2} = \frac{6}{14} \]
- For \(\frac{1}{2}\), multiply the numerator and denominator by 7:
\[ \frac{1 \times 7}{2 \times 7} = \frac{7}{14} \]

**Hint:** When converting fractions, ensure that you multiply both the numerator and denominator by the same number to keep the value of the fraction unchanged.

### Step 4: Add the fractions
Now we can add the two fractions:
\[ \frac{6}{14} + \frac{7}{14} = \frac{6 + 7}{14} = \frac{13}{14} \]

**Hint:** When adding fractions with the same denominator, simply add the numerators and keep the denominator the same.

### Step 5: Divide by \(\frac{7}{8}\)
Now we need to divide \(\frac{13}{14}\) by \(\frac{7}{8}\). To divide by a fraction, we multiply by its reciprocal:
\[ \frac{13}{14} \div \frac{7}{8} = \frac{13}{14} \times \frac{8}{7} \]

**Hint:** The reciprocal of a fraction \(\frac{a}{b}\) is \(\frac{b}{a}\).

### Step 6: Multiply the fractions
Now, we multiply:
\[ \frac{13 \times 8}{14 \times 7} = \frac{104}{98} \]

**Hint:** When multiplying fractions, multiply the numerators together and the denominators together.

### Step 7: Simplify the result
Now we simplify \(\frac{104}{98}\). Both numbers can be divided by 2:
\[ \frac{104 \div 2}{98 \div 2} = \frac{52}{49} \]

**Hint:** To simplify a fraction, divide both the numerator and denominator by their greatest common divisor (GCD).

### Final Answer
The simplified result of \((\frac{3}{7} + \frac{1}{2}) \div \frac{7}{8}\) is \(\frac{52}{49}\).

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