Evaluate the following :
(i) `4/5 div 3" (ii) "7/8 div 5/6" (iii) " 5""1/3 div 4/15`.

Answer

Let's solve the given problems step by step.

### (i) Evaluate `4/5 div 3`

1. **Convert the division to multiplication**:
\[ \frac{4}{5} \div 3 = \frac{4}{5} \div \frac{3}{1} \]
Here, we write 3 as a fraction \(\frac{3}{1}\).

2. **Change the division to multiplication**:
\[ \frac{4}{5} \times \frac{1}{3} \]
We change the divisor (3) to its reciprocal (1/3).

3. **Multiply the fractions**:
\[ \frac{4 \times 1}{5 \times 3} = \frac{4}{15} \]

**Final Answer for (i)**: \(\frac{4}{15}\)

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### (ii) Evaluate `7/8 div 5/6`

1. **Convert the division to multiplication**:
\[ \frac{7}{8} \div \frac{5}{6} \]

2. **Change the division to multiplication**:
\[ \frac{7}{8} \times \frac{6}{5} \]
Here, we take the reciprocal of \(\frac{5}{6}\).

3. **Multiply the fractions**:
\[ \frac{7 \times 6}{8 \times 5} = \frac{42}{40} \]

4. **Simplify the fraction**:
\[ \frac{42 \div 2}{40 \div 2} = \frac{21}{20} \]

**Final Answer for (ii)**: \(\frac{21}{20}\)

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### (iii) Evaluate `5 1/3 div 4/15`

1. **Convert the mixed number to an improper fraction**:
\[ 5 \frac{1}{3} = \frac{5 \times 3 + 1}{3} = \frac{15 + 1}{3} = \frac{16}{3} \]

2. **Convert the division to multiplication**:
\[ \frac{16}{3} \div \frac{4}{15} \]

3. **Change the division to multiplication**:
\[ \frac{16}{3} \times \frac{15}{4} \]
We take the reciprocal of \(\frac{4}{15}\).

4. **Multiply the fractions**:
\[ \frac{16 \times 15}{3 \times 4} \]

5. **Simplify before multiplying**:
- \(16 \div 4 = 4\)
- \(15 \div 3 = 5\)

So, we have:
\[ \frac{4 \times 5}{1 \times 1} = \frac{20}{1} = 20 \]

**Final Answer for (iii)**: \(20\)

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### Summary of Answers:
- (i) \(\frac{4}{15}\)
- (ii) \(\frac{21}{20}\)
- (iii) \(20\)

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