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Evaluate: (i) 5/6-7/8, (ii) 5/12 -17/1...

Evaluate:
(i) `5/6-7/8`, (ii) `5/12 -17/18`, (iii) `11/15 - 13/20`, (iv) `-5/9 - (-2/3)`, (v) `6/11 -(-3/4)`, (vi) `-2/3 -3/4`

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The correct Answer is:
Let's evaluate each part of the question step by step. ### (i) Evaluate \( \frac{5}{6} - \frac{7}{8} \) 1. **Find the LCM of the denominators (6 and 8)**: - The multiples of 6 are 6, 12, 18, 24, ... - The multiples of 8 are 8, 16, 24, ... - The LCM is **24**. 2. **Convert each fraction to have the common denominator**: - \( \frac{5}{6} = \frac{5 \times 4}{6 \times 4} = \frac{20}{24} \) - \( \frac{7}{8} = \frac{7 \times 3}{8 \times 3} = \frac{21}{24} \) 3. **Subtract the fractions**: - \( \frac{20}{24} - \frac{21}{24} = \frac{20 - 21}{24} = \frac{-1}{24} \) **Final Answer for (i)**: \( \frac{-1}{24} \) ### (ii) Evaluate \( \frac{5}{12} - \frac{17}{18} \) 1. **Find the LCM of the denominators (12 and 18)**: - The multiples of 12 are 12, 24, 36, ... - The multiples of 18 are 18, 36, ... - The LCM is **36**. 2. **Convert each fraction to have the common denominator**: - \( \frac{5}{12} = \frac{5 \times 3}{12 \times 3} = \frac{15}{36} \) - \( \frac{17}{18} = \frac{17 \times 2}{18 \times 2} = \frac{34}{36} \) 3. **Subtract the fractions**: - \( \frac{15}{36} - \frac{34}{36} = \frac{15 - 34}{36} = \frac{-19}{36} \) **Final Answer for (ii)**: \( \frac{-19}{36} \) ### (iii) Evaluate \( \frac{11}{15} - \frac{13}{20} \) 1. **Find the LCM of the denominators (15 and 20)**: - The multiples of 15 are 15, 30, 45, 60, ... - The multiples of 20 are 20, 40, 60, ... - The LCM is **60**. 2. **Convert each fraction to have the common denominator**: - \( \frac{11}{15} = \frac{11 \times 4}{15 \times 4} = \frac{44}{60} \) - \( \frac{13}{20} = \frac{13 \times 3}{20 \times 3} = \frac{39}{60} \) 3. **Subtract the fractions**: - \( \frac{44}{60} - \frac{39}{60} = \frac{44 - 39}{60} = \frac{5}{60} \) - Simplifying \( \frac{5}{60} \) gives \( \frac{1}{12} \). **Final Answer for (iii)**: \( \frac{1}{12} \) ### (iv) Evaluate \( -\frac{5}{9} - (-\frac{2}{3}) \) 1. **Rewrite the expression**: - \( -\frac{5}{9} + \frac{2}{3} \) 2. **Find the LCM of the denominators (9 and 3)**: - The multiples of 9 are 9, 18, ... - The multiples of 3 are 3, 6, 9, ... - The LCM is **9**. 3. **Convert each fraction to have the common denominator**: - \( -\frac{5}{9} \) remains \( -\frac{5}{9} \) - \( \frac{2}{3} = \frac{2 \times 3}{3 \times 3} = \frac{6}{9} \) 4. **Add the fractions**: - \( -\frac{5}{9} + \frac{6}{9} = \frac{-5 + 6}{9} = \frac{1}{9} \) **Final Answer for (iv)**: \( \frac{1}{9} \) ### (v) Evaluate \( \frac{6}{11} - (-\frac{3}{4}) \) 1. **Rewrite the expression**: - \( \frac{6}{11} + \frac{3}{4} \) 2. **Find the LCM of the denominators (11 and 4)**: - The multiples of 11 are 11, 22, 33, ... - The multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, ... - The LCM is **44**. 3. **Convert each fraction to have the common denominator**: - \( \frac{6}{11} = \frac{6 \times 4}{11 \times 4} = \frac{24}{44} \) - \( \frac{3}{4} = \frac{3 \times 11}{4 \times 11} = \frac{33}{44} \) 4. **Add the fractions**: - \( \frac{24}{44} + \frac{33}{44} = \frac{24 + 33}{44} = \frac{57}{44} \) **Final Answer for (v)**: \( \frac{57}{44} \) ### (vi) Evaluate \( -\frac{2}{3} - \frac{3}{4} \) 1. **Find the LCM of the denominators (3 and 4)**: - The multiples of 3 are 3, 6, 9, 12, ... - The multiples of 4 are 4, 8, 12, ... - The LCM is **12**. 2. **Convert each fraction to have the common denominator**: - \( -\frac{2}{3} = -\frac{2 \times 4}{3 \times 4} = -\frac{8}{12} \) - \( -\frac{3}{4} = -\frac{3 \times 3}{4 \times 3} = -\frac{9}{12} \) 3. **Add the fractions**: - \( -\frac{8}{12} - \frac{9}{12} = \frac{-8 - 9}{12} = \frac{-17}{12} \) **Final Answer for (vi)**: \( \frac{-17}{12} \) ---
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