Question

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

Answer 1

It takes three copies of 1/6 to equal one copy of 1/2 because 1/2 is equivalent to 3/6 when both fractions are expressed with a common denominator of 6.

Step-by-step explanation:

To understand why it takes three copies of 1/6 to show the same amount as one copy of 1/2, let's look at the denominators. The number 6 is the least common multiple of 2 and 6. So, to compare them on the same scale, we convert 1/2 into sixths by finding an equivalent fraction that has 6 as the denominator. Doing this, we see that 1/2 is the same as 3/6 because if you multiply both the numerator (the top of the fraction) and the denominator (the bottom of the fraction) by 3, you get 3/6. Now it's clear that 1/2 (which is now shown as 3/6) is equal in value to 3 copies of 1/6, because both represent three sixths of a whole.

Answer 2

Because 3/6 is equal to 1/2.
You multiply the 1 (in 1/2) by 3, and the 2 (in 1/2) by 3 to get 3/6. You need to have a common denominator, and 6 was the common denominator.