If three(3) times a number is greater than 
one half(1/2) by forty five(45). What is the number

In the sentence:

...3 times a number is greater than 1/2 by 45.

Replace the words "a number" by x.

...3 times x is greater than 1/2 by forty five(45).

Replace the words "3 times x" by 3x:

...3x is greater than 1/2 by 45.

To make 1/2 greater by 45, add 45 to it, getting 1/2 + 45
So replace "greater than 1/2 by 45" by 1/2 + 45

...3x is 1/2 + 45...

Replace the "is" by an equal sign

...3x = 1/2 + 45

Multiply every term by 2 to clear of fractions:

 2·3x = 2·1/2 + 2·45 

   6x = 1 + 90

   6x = 91

Divide both sides by 6

    x = 91/6 or 15 1/6

Check: 

3 times 91/6 is 91/2 or 45 1/2

and that is indeed 45 greater than 1/2.

Edwin