what is the fraction 1620 over 22500 simplified?

1620/22500

 

In this case, think of division.

 

First off, we can tell that the numbers are at least divisible by 10, because both of them end in a 0.

 

162/2250

 

Next, both numbers end in an even number. So, we can divide by 2.

 

81/1125

 

Next is a little trick I learned early on that helped. Add up all of the digits in a number, and divide by 3. If you eventually get all of the digits added and divided and they are equal to 3, 6, or 9 at the end of it, the number is divisible by 3.

 

For instance, 81. 8 and 1. 8 + 1 = 9. This number is divisible by 3.

 

Next, 1125. 1, 1, 2, and 5. 1 + 1 + 2 + 5 = 2 + 2 + 5 = 4 + 5 = 9. This number is divisible by 3 as well.

 

27/375

 

Try it again.

 

27. 2 and 7. 2 + 7 = 9. This number is divisible by 3.

 

375. 3, 7, and 5. 3 + 7 + 5 = 10 + 5 = 15.

15. 1 and 5. 1 + 5 = 6

This number is divisible by 3.

 

9/125

 

Try it again.

 

9. This number is divisible by 3.

 

125. 1, 2, and 5. 1 + 2 + 5 = 3 + 5 = 8. This number is not divisible by 3.

 

Because 125 is not divisible by 3, it cannot be divisible by 9 either, and because the only factors of 9 are 1, 3, and 9, this is the furthest simplified this fraction will become.

 

Going over this again with a calculator, $${\frac{{\mathtt{1\,620}}}{{\mathtt{22\,500}}}} = {\frac{{\mathtt{9}}}{{\mathtt{125}}}} = {\mathtt{0.072}}$$

 

Final answer: 9/125