Question

(1\2-1\3):(1\3-1\4)*(1\4-1\5):(1\5-1\6)=

Answer 1

1/2 - 1/3 = 3/6 - 2/6 = 1/6
1/3 - 1/4 = 4/12 - 3/12 = 1/12
1/6 : 1/12 = 1/6 * 12 = 2
1/4 - 1/5 = 5/20 - 4/20 = 1/20
2* 1/20 = 1/10
1/5 - 1/6 = 6/30 - 5/30 = 1/30
1/10 : 1/30 = 1/10 * 30 = 3 
Отв 3

Answer 2

Let's simplify the expression step by step:

(1/2 - 1/3) : (1/3 - 1/4) * (1/4 - 1/5) : (1/5 - 1/6)

First, let's simplify the fractions within the parentheses:

(3/6 - 2/6) : (4/12 - 3/12) * (3/12 - 2/12) : (2/10 - 1/10)

Now, perform the subtraction:

(1/6) : (1/12) * (1/12) : (1/10)

Next, invert the division to multiplication by taking the reciprocal of the second fraction:

(1/6) * (12/1) * (1/12) * (10/1)

Now, multiply the fractions:

(1/6) * (12/1) * (1/12) * (10/1) = (1/6) * (1) * (1/12) * (10) = (1/6) * (1/12) * (10) = (1/72) * (10) = 10/72

Finally, simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 2:

(10/2) / (72/2) = 5/36

So, the simplified value of the expression is 5/36.