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11. \( \frac{1}{3}+\frac{5}{6}-\frac{7}{12} \) 12. \( \frac{3}{8}-\frac{1}{4}+\frac{5}{16} \) 13. \( \frac{4}{9}+\frac{2}{3}-\frac{5}{18} \) 14. \( \frac{5}{7}-\frac{2}{14}+\frac{3}{28} \) 15. \( \frac{2}{5}+\frac{3}{10}-\frac{1}{20} \) 16. \( \frac{7}{12}-\frac{1}{6}+\frac{5}{24} \) 17. \( \frac{3}{5}+\frac{7}{10}-\frac{9}{20} \) 18. \( \frac{5}{8}-\frac{1}{4}+\frac{3}{16} \) 19. \( \frac{4}{15}+\frac{2}{5}-\frac{7}{30} \) 20. \( \frac{9}{14}-\frac{3}{7}+\frac{5}{28} \)

Ask by Patel Rogers. in Colombia
Feb 26,2025

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Tutor-Verified Answer

Answer

11. 7/12 12. 7/16 13. 5/6 14. 19/28 15. 13/20 16. 5/8 17. 17/20 18. 9/16 19. 13/30 20. 11/28

Solution

A continuación se muestran los pasos para resolver cada fracción: 11. (1/3) + (5/6) – (7/12)  • Se utiliza como denominador común 12.  • 1/3 = 4/12, 5/6 = 10/12 y 7/12 permanece igual.  • Suma: (4 + 10 – 7) / 12 = 7/12 12. (3/8) – (1/4) + (5/16)  • Se utiliza como denominador común 16.  • 3/8 = 6/16, 1/4 = 4/16 y 5/16 permanece igual.  • Suma: (6 – 4 + 5) / 16 = 7/16 13. (4/9) + (2/3) – (5/18)  • Se utiliza como denominador común 18.  • 4/9 = 8/18, 2/3 = 12/18 y 5/18 permanece igual.  • Suma: (8 + 12 – 5) / 18 = 15/18 = 5/6 14. (5/7) – (2/14) + (3/28)  • Se utiliza como denominador común 28.  • 5/7 = 20/28, 2/14 = 4/28 y 3/28 permanece igual.  • Suma: (20 – 4 + 3) / 28 = 19/28 15. (2/5) + (3/10) – (1/20)  • Se utiliza como denominador común 20.  • 2/5 = 8/20, 3/10 = 6/20 y 1/20 permanece igual.  • Suma: (8 + 6 – 1) / 20 = 13/20 16. (7/12) – (1/6) + (5/24)  • Se utiliza como denominador común 24.  • 7/12 = 14/24, 1/6 = 4/24 y 5/24 permanece igual.  • Suma: (14 – 4 + 5) / 24 = 15/24 = 5/8 17. (3/5) + (7/10) – (9/20)  • Se utiliza como denominador común 20.  • 3/5 = 12/20, 7/10 = 14/20 y 9/20 permanece igual.  • Suma: (12 + 14 – 9) / 20 = 17/20 18. (5/8) – (1/4) + (3/16)  • Se utiliza como denominador común 16.  • 5/8 = 10/16, 1/4 = 4/16 y 3/16 permanece igual.  • Suma: (10 – 4 + 3) / 16 = 9/16 19. (4/15) + (2/5) – (7/30)  • Se utiliza como denominador común 30.  • 4/15 = 8/30, 2/5 = 12/30 y 7/30 permanece igual.  • Suma: (8 + 12 – 7) / 30 = 13/30 20. (9/14) – (3/7) + (5/28)  • Se utiliza como denominador común 28.  • 9/14 = 18/28, 3/7 = 12/28 y 5/28 permanece igual.  • Suma: (18 – 12 + 5) / 28 = 11/28 Resumiendo, las respuestas son: 11. 7/12 12. 7/16 13. 5/6 14. 19/28 15. 13/20 16. 5/8 17. 17/20 18. 9/16 19. 13/30 20. 11/28

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Extra Insights

To tackle the addition and subtraction of fractions, it helps to first find a common denominator, which allows for easy combining of the numerators. For instance, in the first problem, the denominators are 3, 6, and 12; the least common multiple (LCM) is 12. By converting each fraction to have the same denominator, you can combine them seamlessly and simplify the final result! When working with fractions, a common mistake is forgetting to adjust all fractions to the common denominator before combining them. Always double-check your calculations, especially when reducing fractions afterward, as it's easy to misplace a number or overlook simplification steps. An effective strategy is to write the entire equation out step-by-step to minimize errors!

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