Simplify
Q`4/7-:9/14`
(ii)`7/10-:3/5`
(iii)`8/9-:16`
(iv)`9-:1/3`
(v)`24-:6/7`
(vi)`3 3/5-:4/5`
(vii)`3 3/7-:8/21`
(viii)`5 4/7-:1 3/10`
(ix)`15 3/7-:1 23/49`

Answer

Let's simplify each part step by step.

### (i) \( \frac{4}{7} \div \frac{9}{14} \)

1. **Convert Division to Multiplication**:
\[ \frac{4}{7} \div \frac{9}{14} = \frac{4}{7} \times \frac{14}{9} \]

2. **Multiply the Fractions**:
\[ = \frac{4 \times 14}{7 \times 9} = \frac{56}{63} \]

3. **Simplify the Fraction**:
\[ = \frac{8}{9} \quad (\text{by dividing both numerator and denominator by 7}) \]

### (ii) \( \frac{7}{10} \div \frac{3}{5} \)

1. **Convert Division to Multiplication**:
\[ \frac{7}{10} \div \frac{3}{5} = \frac{7}{10} \times \frac{5}{3} \]

2. **Multiply the Fractions**:
\[ = \frac{7 \times 5}{10 \times 3} = \frac{35}{30} \]

3. **Simplify the Fraction**:
\[ = \frac{7}{6} \quad (\text{by dividing both numerator and denominator by 5}) \]

### (iii) \( \frac{8}{9} \div 16 \)

1. **Convert 16 to Fraction**:
\[ 16 = \frac{16}{1} \]

2. **Convert Division to Multiplication**:
\[ \frac{8}{9} \div \frac{16}{1} = \frac{8}{9} \times \frac{1}{16} \]

3. **Multiply the Fractions**:
\[ = \frac{8 \times 1}{9 \times 16} = \frac{8}{144} \]

4. **Simplify the Fraction**:
\[ = \frac{1}{18} \quad (\text{by dividing both numerator and denominator by 8}) \]

### (iv) \( 9 \div \frac{1}{3} \)

1. **Convert 9 to Fraction**:
\[ 9 = \frac{9}{1} \]

2. **Convert Division to Multiplication**:
\[ \frac{9}{1} \div \frac{1}{3} = \frac{9}{1} \times \frac{3}{1} \]

3. **Multiply the Fractions**:
\[ = \frac{9 \times 3}{1 \times 1} = \frac{27}{1} \]

4. **Simplify**:
\[ = 27 \]

### (v) \( 24 \div \frac{6}{7} \)

1. **Convert 24 to Fraction**:
\[ 24 = \frac{24}{1} \]

2. **Convert Division to Multiplication**:
\[ \frac{24}{1} \div \frac{6}{7} = \frac{24}{1} \times \frac{7}{6} \]

3. **Multiply the Fractions**:
\[ = \frac{24 \times 7}{1 \times 6} = \frac{168}{6} \]

4. **Simplify the Fraction**:
\[ = 28 \]

### (vi) \( 3 \frac{3}{5} \div \frac{4}{5} \)

1. **Convert Mixed Number to Improper Fraction**:
\[ 3 \frac{3}{5} = \frac{18}{5} \]

2. **Convert Division to Multiplication**:
\[ \frac{18}{5} \div \frac{4}{5} = \frac{18}{5} \times \frac{5}{4} \]

3. **Multiply the Fractions**:
\[ = \frac{18 \times 5}{5 \times 4} = \frac{18}{4} \]

4. **Simplify the Fraction**:
\[ = \frac{9}{2} \]

### (vii) \( 3 \frac{3}{7} \div \frac{8}{21} \)

1. **Convert Mixed Number to Improper Fraction**:
\[ 3 \frac{3}{7} = \frac{24}{7} \]

2. **Convert Division to Multiplication**:
\[ \frac{24}{7} \div \frac{8}{21} = \frac{24}{7} \times \frac{21}{8} \]

3. **Multiply the Fractions**:
\[ = \frac{24 \times 21}{7 \times 8} = \frac{504}{56} \]

4. **Simplify the Fraction**:
\[ = 9 \]

### (viii) \( 5 \frac{4}{7} \div 1 \frac{3}{10} \)

1. **Convert Mixed Numbers to Improper Fractions**:
\[ 5 \frac{4}{7} = \frac{39}{7}, \quad 1 \frac{3}{10} = \frac{13}{10} \]

2. **Convert Division to Multiplication**:
\[ \frac{39}{7} \div \frac{13}{10} = \frac{39}{7} \times \frac{10}{13} \]

3. **Multiply the Fractions**:
\[ = \frac{39 \times 10}{7 \times 13} = \frac{390}{91} \]

4. **Simplify the Fraction**:
\[ = \frac{390}{91} \quad (\text{already in simplest form}) \]

### (ix) \( 15 \frac{3}{7} \div 1 \frac{23}{49} \)

1. **Convert Mixed Numbers to Improper Fractions**:
\[ 15 \frac{3}{7} = \frac{108}{7}, \quad 1 \frac{23}{49} = \frac{72}{49} \]

2. **Convert Division to Multiplication**:
\[ \frac{108}{7} \div \frac{72}{49} = \frac{108}{7} \times \frac{49}{72} \]

3. **Multiply the Fractions**:
\[ = \frac{108 \times 49}{7 \times 72} \]

4. **Simplify the Fraction**:
\[ = \frac{108 \times 7}{7 \times 72} = \frac{108}{72} = \frac{3}{2} \]

### Summary of Answers:
1. \( \frac{8}{9} \)
2. \( \frac{7}{6} \)
3. \( \frac{1}{18} \)
4. \( 27 \)
5. \( 28 \)
6. \( \frac{9}{2} \)
7. \( 9 \)
8. \( \frac{390}{91} \)
9. \( \frac{3}{2} \)