Step-by-step explanation: To order these fractions from least to greatest, we can convert these fractions into percents and it will be easier to see.
Let's start with the fraction 1/3. To write a fraction as a percent, first remember that a percent is a ratio of a number to 100. So to write 1/3 as a percent, we need to find a fraction that is equivalent to 1/3 that has a 100 in the denominator. We can do this by setting up a proportion.
[tex]\frac{1}{3} = \frac{n}{100}[/tex]
Now we can use cross products to find the missing value.
3n = 100
÷3 ÷3
n = 33.3%
We can write 2/7 as a percent by setting up a proportion.
[tex]\frac{2}{7} =\frac{n}{100}[/tex]
Now we can use cross products to find the missing value.
7n = 200
÷7 ÷7
n = 28.5714286%
We can write 3/14 as a percent by setting up a proportion.
[tex]\frac{3}{14} = \frac{n}{100}[/tex]
Now we can use cross products to find the missing value.
14n = 300
÷14 ÷14
n = 21.4285714%
We can write 1/6 as a percent by setting up a proportion.
[tex]\frac{1}{6} = \frac{n}{100}[/tex]
6n = 100
÷6 ÷6
n =16.7%
Now, we can order these percents easier than if we were dealing with fractions.
Now, we can see that 1/6 < 3/14 < 2/7 < 1/3.
