Question

10/(2 12/7 +1 5/17)-(3 4/5+1 3/5)/6

Answer 1

Первым действием найдём сумму дробей в первых скобках:
2 12/17+1 5/17 = 3 (12 + 5)/17 = 3 17/17 = 4.
Вторым действием найдём сумму дробей во вторых скобках:
3 4/5+1 3/5 = 4 (4 + 3)/5 = 4 7/5 = 5 2/5.
Третьим действием найдём частное двух чисел:
10 / 4 = 5/2.
Четвёртым действием найдём частное двух чисел:
(5 2/5) / 6 = (27/5) / (6/1) = (27/5) * (1/6) = (27 * 1) / (5 * 6) = 27/30.
Пятым действием найдём разность двух чисел:
5/2 - 27/30 = (75 - 27) / 30 = 48/30 = 24/15 = 8/5 = 1 3/5.
Правильный ответ: 1 3/5.

Answer 2

To solve this expression, we need to perform the operations in the correct order using the rules of arithmetic. Here is the step-by-step solution:

1. Let's first simplify the mixed numbers by converting them into improper fractions:

2 12/7 = (2*7 + 12)/7 = 26/7

1 5/17 = (1*17 + 5)/17 = 22/17

3 4/5 = (3*5 + 4)/5 = 19/5

1 3/5 = (1*5 + 3)/5 = 8/5

2. Now, let's substitute the simplified fractions into the expression:

10/(26/7 + 1) - ((19/5 + 8/5)/6)

3. Let's simplify the fractions inside the parentheses first:

(19/5 + 8/5) = 27/5

4. Now, let's simplify the expression inside the first set of parentheses by finding a common denominator:

10/(26/7 + 1) = 10/((26/7)*(7/7) + 7/7) = 10/(190/49)

5. Let's invert the fraction and multiply it with 10:

10/(190/49) = 10*(49/190) = 490/190

6. Now, let's simplify the expression by dividing the numerator and denominator by their greatest common factor:

490/190 = (2577)/(25*19) = 49/19

7. Let's substitute this value back into the original expression:

49/19 - (27/5)/6

8. Now, let's simplify the fraction inside the second set of parentheses by multiplying it with the reciprocal of 6:

(27/5)/6 = (27/5)*(1/6) = 9/10

9. Now, let's subtract the two fractions:

49/19 - 9/10

10. Let's find a common denominator:

(49/19)(10/10) - (9/10)(19/19) = (490/190) - (171/190)

11. Let's subtract the numerators:

(490 - 171)/190 = 319/190

Therefore, the solution to the expression is 319/190.