Subtract:
(i) `(3)/(4)` from `(1)/(3)`
(ii) `(-5)/(6)` from `(1)/(3)`
(iii) `(-8)/(9)` from `(-3)/(5)`
(iv) `(-9)/(7)` from -1
(v) `(-18)/(11)` from 1
(vi) `(-13)/(9)` from 0
(vii) `(-32)/(13)` form `(-6)/(5)`
(viii) -7 from `(-4)/(7)`

Answer

Let's solve the problems step by step.

### (i) Subtract \( \frac{3}{4} \) from \( \frac{1}{3} \)

1. Write the expression:
\[ \frac{1}{3} - \frac{3}{4} \]

2. Find the LCM of the denominators (3 and 4):
- The LCM of 3 and 4 is 12.

3. Convert both fractions to have the same denominator:
\[ \frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12} \]
\[ \frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12} \]

4. Now, subtract the fractions:
\[ \frac{4}{12} - \frac{9}{12} = \frac{4 - 9}{12} = \frac{-5}{12} \]

### Answer for (i):
\[ \frac{-5}{12} \]

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### (ii) Subtract \( \frac{-5}{6} \) from \( \frac{1}{3} \)

1. Write the expression:
\[ \frac{1}{3} - \left(-\frac{5}{6}\right) \]

2. This is equivalent to:
\[ \frac{1}{3} + \frac{5}{6} \]

3. Find the LCM of the denominators (3 and 6):
- The LCM of 3 and 6 is 6.

4. Convert \( \frac{1}{3} \):
\[ \frac{1}{3} = \frac{1 \times 2}{3 \times 2} = \frac{2}{6} \]

5. Now, add the fractions:
\[ \frac{2}{6} + \frac{5}{6} = \frac{2 + 5}{6} = \frac{7}{6} \]

### Answer for (ii):
\[ \frac{7}{6} \]

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### (iii) Subtract \( \frac{-8}{9} \) from \( \frac{-3}{5} \)

1. Write the expression:
\[ \frac{-3}{5} - \left(-\frac{8}{9}\right) \]

2. This is equivalent to:
\[ \frac{-3}{5} + \frac{8}{9} \]

3. Find the LCM of the denominators (5 and 9):
- The LCM of 5 and 9 is 45.

4. Convert both fractions:
\[ \frac{-3}{5} = \frac{-3 \times 9}{5 \times 9} = \frac{-27}{45} \]
\[ \frac{8}{9} = \frac{8 \times 5}{9 \times 5} = \frac{40}{45} \]

5. Now, add the fractions:
\[ \frac{-27}{45} + \frac{40}{45} = \frac{-27 + 40}{45} = \frac{13}{45} \]

### Answer for (iii):
\[ \frac{13}{45} \]

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### (iv) Subtract \( \frac{-9}{7} \) from -1

1. Write the expression:
\[ -1 - \left(-\frac{9}{7}\right) \]

2. This is equivalent to:
\[ -1 + \frac{9}{7} \]

3. Write -1 as a fraction:
\[ -1 = \frac{-7}{7} \]

4. Now, add the fractions:
\[ \frac{-7}{7} + \frac{9}{7} = \frac{-7 + 9}{7} = \frac{2}{7} \]

### Answer for (iv):
\[ \frac{2}{7} \]

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### (v) Subtract \( \frac{-18}{11} \) from 1

1. Write the expression:
\[ 1 - \left(-\frac{18}{11}\right) \]

2. This is equivalent to:
\[ 1 + \frac{18}{11} \]

3. Write 1 as a fraction:
\[ 1 = \frac{11}{11} \]

4. Now, add the fractions:
\[ \frac{11}{11} + \frac{18}{11} = \frac{11 + 18}{11} = \frac{29}{11} \]

### Answer for (v):
\[ \frac{29}{11} \]

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### (vi) Subtract \( \frac{-13}{9} \) from 0

1. Write the expression:
\[ 0 - \left(-\frac{13}{9}\right) \]

2. This is equivalent to:
\[ 0 + \frac{13}{9} = \frac{13}{9} \]

### Answer for (vi):
\[ \frac{13}{9} \]

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### (vii) Subtract \( \frac{-32}{13} \) from \( \frac{-6}{5} \)

1. Write the expression:
\[ \frac{-6}{5} - \left(-\frac{32}{13}\right) \]

2. This is equivalent to:
\[ \frac{-6}{5} + \frac{32}{13} \]

3. Find the LCM of the denominators (5 and 13):
- The LCM of 5 and 13 is 65.

4. Convert both fractions:
\[ \frac{-6}{5} = \frac{-6 \times 13}{5 \times 13} = \frac{-78}{65} \]
\[ \frac{32}{13} = \frac{32 \times 5}{13 \times 5} = \frac{160}{65} \]

5. Now, add the fractions:
\[ \frac{-78}{65} + \frac{160}{65} = \frac{-78 + 160}{65} = \frac{82}{65} \]

### Answer for (vii):
\[ \frac{82}{65} \]

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### (viii) Subtract -7 from \( \frac{-4}{7} \)

1. Write the expression:
\[ \frac{-4}{7} - (-7) \]

2. This is equivalent to:
\[ \frac{-4}{7} + 7 \]

3. Write 7 as a fraction:
\[ 7 = \frac{49}{7} \]

4. Now, add the fractions:
\[ \frac{-4}{7} + \frac{49}{7} = \frac{-4 + 49}{7} = \frac{45}{7} \]

### Answer for (viii):
\[ \frac{45}{7} \]

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