Finding Common Denominators to Compare Fractions

Let's compare fractions with different denominators using equivalent fractions.

Sometimes you can tell which fraction is greater just by looking at a diagram.

For example, when comparing 1/2 and 2 fths, 1/2 clearly shows more area shaded in. So 1/2 is greater than 2 fths. But what about comparing 2/3 and 3/4s? Visually, they look very close. 3/4s looks greater since the unshaded area is smaller.

But let's look at a more precise method that can confirm this. A way to compare any two fractions is to find a common denominator. This means we'll rewrite each fraction as an equivalent one but with the same bottom number. For/ thirds and fourths, a good common denominator is 12. Since both 3 and 4 are factors of 12, let's start with 2/3. To turn it into 12ths, we can see that we need to multiply the denominator 3 by 4. To keep the fraction equivalent, we must also multiply the numerator 2 by 4. That gives us 8 12ths. Now, let's do the same for 3/4s. To turn the denominator 4 into 12, we multiply by 3. So we must also multiply the numerator 3 by 3. This gives us 9 12ths. Now the comparison is simple. Which is greater 8 12ths or 92ths? Since 9 is greater than 8, we know that 92ths is the larger fraction.

This means that 3/4s is greater than 2/3. Finding a common denominator helps you compare fractions accurately just by looking at the numerators. This strategy works for any pair of fractions.