Question

What is 9 1/6 - 5 5/5

Answer 1

Here is your equation:

`9 (1)/(6) - 5 (5)/(5)`

To subtract fractions, the denominator must be the same. The denominator is the bottom number in the fraction. The 2 denominators are 5 and 6. In order to make them the same, you have to find the LCM OF 5 and 6. To find it, list the multiples of both numbers and see which is common.

`5- 5, 10, 15, 20, 25,\bf30`

`6-6, 12, 18, 24,\bf 30`

The LCM of 5 and 6 is 30. Now change the mixed numbers so that they have common denominators.

`9 (1 * 5)/(6 * 5) = 9 (5)/(30)`

`5 (5 * 6)/(5 * 6) = 5 (30)/(30)`

Here is your new equation:

`9 (5)/(30) - 5 (30)/(30)`

Now you have a problem. You're subtracting a smaller fraction from a bigger fraction. That means you need to remove 1 from the whole number and add it to the fraction. Here's how:

`9 (5)/(30) \\ \\9-1 = 8\\ \\ 1 = (30)/(30) \\ \\ (5)/(30) + (30)/(30) = (35)/(30) \\ \\ 8 + (35)/(30) = 8 (35)/(30)`

Here is your new equation:

`8 (35)/(30) - 5 (30)/(30)`

Subtract:

`8 (35)/(30) - 5 (30)/(30) = 3 (5)/(30)`

Since the denominator(top number) is a multiple of the numerator(top number), divide both numbers by the numerator.

`3 (5 / 5)/(30 / 5) = 3 (1)/(6)`

Your answer is
`3`
`(1)/(6)`