Question

Найдите значение выражения: 1)27/34+(1/2-5/17); 2)(5/6-2/7)+(13/15-14/25); 3)17-(19/24-5/18-1/8); 4)(41/42-5/21)-(7/13-5/21)

Answer 1

1) 1
2)299/350
3)133/18
4)239/546

Answer 2

27/34 + (1/2 - 5/17) = 27/34 + (8/17 - 5/17) = 27/34 + 3/17 To add these fractions, we need to find a common denominator, which is 34 × 2 = 68: 27/34 + 3/17 = (27×2)/(34×2) + 3/(17×2) = 54/68 + 3/34 Now that the denominators are the same, we can add the fractions: 54/68 + 3/34 = (54+6)/68 = 60/68 We can simplify this fraction by dividing both the numerator and the denominator by their greatest common factor, which is 4: 60/68 = 15/17 Therefore, 27/34 + (1/2 - 5/17) = 15/17.

(5/6 - 2/7) + (13/15 - 14/25) = 35/42 - 12/42 + 26/30 - 14/25 To add the fractions with unlike denominators, we need to find a common denominator, which is 2 × 3 × 5 × 7 × 25 = 52,500: 35/42 - 12/42 + 26/30 - 14/25 = (35 × 1250)/(42 × 1250) - (12 × 1250)/(42 × 1250) + (26 × 1750)/(30 × 1750) - (14 × 2100)/(25 × 2100) = 43,750/52,500 - 15,000/52,500 + 45,500/52,500 - 29,400/52,500 Now that the denominators are the same, we can add the fractions: 43,750/52,500 - 15,000/52,500 + 45,500/52,500 - 29,400/52,500 = 44,850/52,500 We can simplify this fraction by dividing both the numerator and the denominator by their greatest common factor, which is 150: 44,850/52,500 = 299/350 Therefore, (5/6 - 2/7) + (13/15 - 14/25) = 299/350.

17 - (19/24 - 5/18 - 1/8) = 17 - (19/24 - 10/36 - 3/24) = 17 - (19/24 - 5/12 - 1/8) = 17 - (19×2)/(24×2) + 5×2/(12×2) + 3/(24×3) = 17 - 38/48 + 10/24 + 1/72 Now that the denominators are the same, we can simplify: 17 - 38/48 + 10/24 + 1/72 = 17 - 19/24 + 5/24 + 1/72 = 17 - 14/72 + 5/72 + 1/72 = 17 - 8/72 We can simplify this fraction by dividing both the numerator and the denominator by their greatest common factor, which is 8: 17 - 8/72 = 17 - 1/9 Therefore, 17 - (19/24 - 5/18 - 1/8) = 17 - 1/