We need to first find the common denominator for all four fractions. To do this, let's look at the multiples of each number. You have to find the smallest number that occurs for all four numbers. HOWEVER, in this case, listing out the factors would be pointless since the numbers are so far apart from one another. I took the time to do it in my head and the least common denominator is apparently 420.
So we need to multiply the denominators in such a way where they all become 420.
For 2/7, what can we multiply to 7 to make it 420? Well, 420 divided by 7 equals 60, so that's the number we need to use.
2/7 = (2 * 60)/(7 * 60) = 120/420 <- This is our first fraction
For 2/15, what can we multiply to 15 to make it 420? Well, 420 divided by 15 equals 28, so that's the number we need to use.
2/15 = (2 * 28)/(15 * 28) = 56/420 <- This is our second fraction
For 1/8, what can we multiply to 8 to make it 420? Well, 420 divided by 8 is 52.5, so that's the number we need to use. (It may be a decimal, but it's not a complicated one so we can solve this problem using that instead)
1/8 = (1 * 52.5)/(8 * 52.5) = 52.5/420 <- This is our third fraction
For 1/4, what can we multiply to 4 to make it 420? Well, 420 divided by 4 is 105, so that's the number we need to use.
1/4 = (1 * 105)/(4 * 105) = 105/420 <- This is our fourth and final fraction
So, using all four fractions, we can now determine which is smallest because they all now have the same common denominator. Look for the smallest number in the numerator for each fraction.
120/420
56/420
52.5/420
105/420
So it's obvious that the third fraction is the smallest, 52.5/420, which we got from 1/8.
So 1/8 is the smallest fraction.
