Why does it take 3 copies of 1/6 to show the same amount as 1 copy of 1/2?

You can solve this by putting the number of copies in the top part of the fraction. If you replace the one in the top part of 1/6 with 3, you get the fraction 3/6. Half of six is three and half of two is one, so both fractions are equal. You can test this be dividing the 3 in the top by 3 and the 6 in the bottom by three. Your result will be 1/2. Although there are three times ad many copies, each copy is three times as small, so it balances out.