Is 1/6 Less Than 32/75?

Are you looking to calculate whether 1/6 is less than 32/75? One of the most common calculations you'll make in math is to compare fractions. In this really simple guide, we'll teach you how to compare and determine if 1/6 is smaller than 32/75 and walk you through the step-by-process of how the calculation is made.

A quick reminder on fractions before we start: the number at the top of the fraction is called the numerator and the number at the bottom of the fraction line is called the denominator.

There are two methods to calculate if 1/6 is smaller than 32/75 and which one you use will depend on the problem you're trying to solve:

Let's start with the first method: converting the fractions to the same denominator. First, we'll set up 1/6 and 32/75 side by side so they are easier to see:

Converting Denominator

1 / 6 & 32 / 75

Our denominators are 6 and 75. What we need to do is find the lowest common denominator of the two numbers. This is the smallest number that can be divided by both 6 and 75. In this case, the lowest common denominator is 150.

If we multiply the first denominator (6) by 25 we will get 150. If we multiply the second denominator (75) by 2 we will also get 150. We also need to multiply the numerators above the line by the same amounts so that the fraction values are correct:

1 x 25 / 6 x 25 32 x 2 / 75 x 2

This is what 1/6 and 32/75 look like with the same denominator:

25 / 150 & 64 / 150

Now that these fractions have been converted to have the same denominator, we can clearly see by looking at the numerators that 25 is less than 64 which also means that 1/6 is less than 32/75.

Converting to Decimal

You can also compare these fractions by first converting them to decimal format. This is a lot faster than working out the lowest common denominator. All we do here is divide the numerator by the denominator for each fraction:

1/6 = 0.1667
32/75 = 0.4267

Now that these fractions have been converted to decimal format, we can compare the numbers to get our answer. 0.1667 is less than 0.4267 which also means that 1/6 is less than 32/75.

Hopefully this tutorial has helped you to understand how to compare fractions and you can use your new found skills to compare whether one fraction is less than another or not!