Explanation

When 5/3 is divided, it gives 1.666..., where 6 repeats infinitely.

Since the decimal never ends but follows a repeating pattern, it is non-terminating and recurring.

Explanation

To find (A ∪ B)':

First, find A ∪ B:

A ∪ B = {2, 3, 4} ∪ {1, 3, 5}

= {1, 2, 3, 4, 5}

Now, find the complement of A ∪ B:

(A ∪ B)' = U - (A ∪ B)

= {1, 2, 3, 4, 5} - {1, 2, 3, 4, 5}

= {}

Explanation

A proper fraction has a numerator smaller than the denominator, meaning its value is less than 1.

7/8 is the only one that meets this condition.

Explanation

1. Multiply the numerators:

   $$2\times 4=8$$

2. Multiply the denominators:

   $$9\times 9=81$$

2/9​×4​/9=8/18​

Explanation

To find the smallest ratio, we need to simplify the fraction 0.35/0.65.

First, convert the decimals to fractions:

0.35 = 35/100 = 7/20

0.65 = 65/100 = 13/20

Now, divide the fractions:

(7/20) ÷ (13/20) = 7/13

So, the smallest ratio is 7/13.

Explanation

Explanation

The complement of a null set (∅) includes all elements of the universal set (U).

Since ∅ contains nothing, its complement is everything in U, so ∅' = U.

Explanation

Let the original bill be x. After deduction of 20%, the remaining amount is Rupees 100. Expressing given information in mathematical form.

x - 20% of x = 100

Solving the mentioned mathematical equation to find the value of x.

x - 20/100x = 100

x - x/5 = 100

Taking L.C.M., which is 5.

5x - x = 5*100

Performing subtraction and multiplication.

4x = 500

Performing division to find the value of x.

x = 500/4

x = Rupees 125

So, the original bill is Rupees 125.

Explanation

To solve the equation, follow the order of operations:

3 × 4 = 12

12 × 5 = 60

60 ÷ 5 = 12

Explanation

12 × 0.012 = 0.144