Evalaute:
(i) `7/12 + -4/3`, (ii) `-12/25 + -5/6`, (iii) `-27/32 + (-9/16)`
(iv) `-18 + 6/5`, (v) `26 + (-1/13)` (vi) `1/25 + -5`

Answer

Let's evaluate each part step by step.

### (i) Evaluate \( \frac{7}{12} + -\frac{4}{3} \)

1. Rewrite the expression:
\[ \frac{7}{12} - \frac{4}{3} \]

2. Find the LCM of the denominators (12 and 3), which is 12.

3. Convert \( \frac{4}{3} \) to have a denominator of 12:
\[ \frac{4}{3} = \frac{4 \times 4}{3 \times 4} = \frac{16}{12} \]

4. Now substitute back into the expression:
\[ \frac{7}{12} - \frac{16}{12} = \frac{7 - 16}{12} = \frac{-9}{12} \]

5. Simplify \( \frac{-9}{12} \):
\[ \frac{-9 \div 3}{12 \div 3} = \frac{-3}{4} \]

**Final Answer for (i):** \( \frac{-3}{4} \)

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### (ii) Evaluate \( -\frac{12}{25} + -\frac{5}{6} \)

1. Rewrite the expression:
\[ -\frac{12}{25} - \frac{5}{6} \]

2. Find the LCM of the denominators (25 and 6), which is 150.

3. Convert \( -\frac{12}{25} \) to have a denominator of 150:
\[ -\frac{12}{25} = -\frac{12 \times 6}{25 \times 6} = -\frac{72}{150} \]

4. Convert \( -\frac{5}{6} \) to have a denominator of 150:
\[ -\frac{5}{6} = -\frac{5 \times 25}{6 \times 25} = -\frac{125}{150} \]

5. Now substitute back into the expression:
\[ -\frac{72}{150} - \frac{125}{150} = \frac{-72 - 125}{150} = \frac{-197}{150} \]

6. Simplify \( \frac{-197}{150} \) (it cannot be simplified further).

**Final Answer for (ii):** \( \frac{-197}{150} \)

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### (iii) Evaluate \( -\frac{27}{32} + (-\frac{9}{16}) \)

1. Rewrite the expression:
\[ -\frac{27}{32} - \frac{9}{16} \]

2. Find the LCM of the denominators (32 and 16), which is 32.

3. Convert \( -\frac{9}{16} \) to have a denominator of 32:
\[ -\frac{9}{16} = -\frac{9 \times 2}{16 \times 2} = -\frac{18}{32} \]

4. Now substitute back into the expression:
\[ -\frac{27}{32} - \frac{18}{32} = \frac{-27 - 18}{32} = \frac{-45}{32} \]

**Final Answer for (iii):** \( \frac{-45}{32} \)

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### (iv) Evaluate \( -18 + \frac{6}{5} \)

1. Rewrite \( -18 \) as a fraction:
\[ -18 = -\frac{18 \times 5}{1 \times 5} = -\frac{90}{5} \]

2. Now substitute back into the expression:
\[ -\frac{90}{5} + \frac{6}{5} = \frac{-90 + 6}{5} = \frac{-84}{5} \]

**Final Answer for (iv):** \( \frac{-84}{5} \)

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### (v) Evaluate \( 26 + (-\frac{1}{13}) \)

1. Rewrite \( 26 \) as a fraction:
\[ 26 = \frac{26 \times 13}{1 \times 13} = \frac{338}{13} \]

2. Now substitute back into the expression:
\[ \frac{338}{13} - \frac{1}{13} = \frac{338 - 1}{13} = \frac{337}{13} \]

**Final Answer for (v):** \( \frac{337}{13} \)

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### (vi) Evaluate \( \frac{1}{25} + -5 \)

1. Rewrite \( -5 \) as a fraction:
\[ -5 = -\frac{5 \times 25}{1 \times 25} = -\frac{125}{25} \]

2. Now substitute back into the expression:
\[ \frac{1}{25} - \frac{125}{25} = \frac{1 - 125}{25} = \frac{-124}{25} \]

**Final Answer for (vi):** \( \frac{-124}{25} \)

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