A number is (1/7) of another number. The difference of the numbers is 18. (Assume that you are subtracting the smaller number from the larger number.) find the numbers.

Start by writing an equation

x - 1/7x = 18

since there is no number in front of the first x it is an implied 1. In order to subtract we need an equivalent fraction with a common denominator so we change 1 to 7/7.

Now we can subtract

7/7x - 1/7x = 18

6/7x = 18

divide each side by 6/7 (multiply 18 * the reciprocal)

x = 18/1 * 7/6

x = 126/6

x = 21