Evaluate:
(i) `2/(-3) + -4/9`, (ii) `=1/2 + -3/4`, (iii) `7/-9 + -5/6`
(iv) `2 + -3/4` , (v) `3 + -5/6`, (vi) `-4 + 2/3`

Answer

Let's evaluate the given expressions step by step.

### (i) Evaluate \( \frac{2}{-3} + \frac{-4}{9} \)

1. Rewrite the expression:
\[ \frac{2}{-3} + \frac{-4}{9} = -\frac{2}{3} - \frac{4}{9} \]

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

3. Convert \(-\frac{2}{3}\) to have a denominator of 9:
\[ -\frac{2}{3} = -\frac{2 \times 3}{3 \times 3} = -\frac{6}{9} \]

4. Now add the fractions:
\[ -\frac{6}{9} - \frac{4}{9} = -\frac{6 + 4}{9} = -\frac{10}{9} \]

**Answer for (i):** \(-\frac{10}{9}\)

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### (ii) Evaluate \( \frac{1}{2} + \frac{-3}{4} \)

1. Rewrite the expression:
\[ \frac{1}{2} + \frac{-3}{4} = \frac{1}{2} - \frac{3}{4} \]

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

3. Convert \(\frac{1}{2}\) to have a denominator of 4:
\[ \frac{1}{2} = \frac{1 \times 2}{2 \times 2} = \frac{2}{4} \]

4. Now subtract the fractions:
\[ \frac{2}{4} - \frac{3}{4} = \frac{2 - 3}{4} = \frac{-1}{4} \]

**Answer for (ii):** \(-\frac{1}{4}\)

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### (iii) Evaluate \( \frac{7}{-9} + \frac{-5}{6} \)

1. Rewrite the expression:
\[ \frac{7}{-9} + \frac{-5}{6} = -\frac{7}{9} - \frac{5}{6} \]

2. Find the LCM of the denominators (9 and 6):
- The LCM of 9 and 6 is 18.

3. Convert \(-\frac{7}{9}\) to have a denominator of 18:
\[ -\frac{7}{9} = -\frac{7 \times 2}{9 \times 2} = -\frac{14}{18} \]

4. Convert \(-\frac{5}{6}\) to have a denominator of 18:
\[ -\frac{5}{6} = -\frac{5 \times 3}{6 \times 3} = -\frac{15}{18} \]

5. Now add the fractions:
\[ -\frac{14}{18} - \frac{15}{18} = -\frac{14 + 15}{18} = -\frac{29}{18} \]

**Answer for (iii):** \(-\frac{29}{18}\)

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### (iv) Evaluate \( 2 + \frac{-3}{4} \)

1. Rewrite the expression:
\[ 2 + \frac{-3}{4} = 2 - \frac{3}{4} \]

2. Convert 2 to a fraction:
\[ 2 = \frac{2 \times 4}{1 \times 4} = \frac{8}{4} \]

3. Now subtract the fractions:
\[ \frac{8}{4} - \frac{3}{4} = \frac{8 - 3}{4} = \frac{5}{4} \]

**Answer for (iv):** \(\frac{5}{4}\)

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### (v) Evaluate \( 3 + \frac{-5}{6} \)

1. Rewrite the expression:
\[ 3 + \frac{-5}{6} = 3 - \frac{5}{6} \]

2. Convert 3 to a fraction:
\[ 3 = \frac{3 \times 6}{1 \times 6} = \frac{18}{6} \]

3. Now subtract the fractions:
\[ \frac{18}{6} - \frac{5}{6} = \frac{18 - 5}{6} = \frac{13}{6} \]

**Answer for (v):** \(\frac{13}{6}\)

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### (vi) Evaluate \( -4 + \frac{2}{3} \)

1. Rewrite the expression:
\[ -4 + \frac{2}{3} = -4 + \frac{2}{3} \]

2. Convert -4 to a fraction:
\[ -4 = \frac{-4 \times 3}{1 \times 3} = \frac{-12}{3} \]

3. Now add the fractions:
\[ \frac{-12}{3} + \frac{2}{3} = \frac{-12 + 2}{3} = \frac{-10}{3} \]

**Answer for (vi):** \(-\frac{10}{3}\)

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