Using Only Five 5's and any mathematical operator make sum as 37

Arrange the numbers 1, 2, 3, 4, 5, 6, 7, 8 and 9 above and below the division line in a manner that the thus formed fractions equal to 1/3.

(You can use one number only once)

Can you solve this tricky maths equation problem by replacing it? mark with the correct symbol?

19834 -----: 187
15921 -----: 153
17561 -----: 139
13734 -----: ???

Look at this sequence from top to bottom. What is the next number in the sequence?
1
11
21
1211
111221
312211

Rectify the following equality 101 - 102 = 1 by moving just one digit.

Can you find out the smallest number that can be conveyed as the sum of three squares in three unique ways?

Replace the 'X' with any mathematical symbol to make the expression equal to 111.

18 X 12 X 2 X 3 = 111

Use the digits from 1 up to 9 and make 100.

Follow the rules.
=> Each digit should be used only once.
=> You can only use addition.
=> For making a number, two single digits can be combined (for example, 4 and 2 can be combined to form 42 or 24)
=> A fraction can also be made by combining the two single digits (for example, 4 and 2 can be combined to form 4/2 or 2/4)

Question: how can we do this?

I am a prime number.
The double of myself is equal to the square of me.

which number am I?

Double it and multiply it by 4. Then divide it by 8 and you’ll have it once more. What number is it?