Question

(1/15-1/16):(1/16-1/17)*(1/17-1/18):(1/18-11/19)=​

Answer 1

Ответ:

19/15

Пошаговое объяснение:

(1/15-1/16):(1/16-1/17)*(1/17-1/18):(1/18-11/19)=17/15*19/17 = 19/15

(1/15-1/16) = 1/15*16

(1/16-1/17) = 1/16*17

(1/15-1/16):(1/16-1/17) = 16*17/16*15 = 17/15

(1/17-1/18) = 1/17*18

(1/18-11/19) = 1/18*19

(1/17-1/18):(1/18-11/19) = 18*19/17*18 = 19/17

Answer 2

To solve this expression, let's break it down step by step:

(1/15 - 1/16) : (1/16 - 1/17) * (1/17 - 1/18) : (1/18 - 11/19)

Step 1: Simplify the fractions within each set of parentheses:

(1/15 - 1/16) = (16/240 - 15/240) = 1/240 (1/16 - 1/17) = (17/272 - 16/272) = 1/272 (1/17 - 1/18) = (18/306 - 17/306) = 1/306 (1/18 - 11/19) = (19/342 - 198/342) = -179/342

Step 2: Substitute the simplified fractions back into the original expression:

(1/240) : (1/272) * (1/306) : (-179/342)

Step 3: Perform the multiplications and divisions:

(1/240) / (1/272) * (1/306) / (-179/342)

Step 4: Invert and multiply when dividing by a fraction:

(1/240) * (272/1) * (1/306) * (-342/179)

Step 5: Multiply the numerators and denominators:

(272/240) * (-342/306) * (-342/179)

Step 6: Simplify fractions:

(17/15) * (-57/51) * (-342/179)

Step 7: Multiply the fractions:

(17 * -57 * -342) / (15 * 51 * 179)

Step 8: Calculate the result:

34722 / 1377955 ≈ 0.0251997

So, the result of the expression is approximately 0.0251997.