How Do You Compare Fractions by Finding a Common Denominator?

If we can make 72 the denominator of both of our fractions, then we'll be able to compare them
Any number divided by itself is 1, so 9/9 is really just 1
Multiplying by 1 does not change the value of the fraction
3/8 becomes the equivalent fraction 27/72
8/8 reduces to 1, so it's also a fancy form of 1
4/9 becomes the equivalent fraction 32/72
The '<' symbol means 'less than'

1. You can always compare two fractions with the same denominator by just looking at their numerators
1. We'll have to multiply each fraction by a special form of 1 to get them to have a common denominator
1. To change the 8 into a 72, we'll need to multiply it by 9
2. Similarly, to change the 9 into a 72, we'll need to multiply it by 8
1. We get equivalent fractions by multiplying the numerator and denominator by the same number
2. So we multiply 3/8 by 9/9 and 4/9 by 8/8
3. Since a number over itself reduces to 1, we're not changing the value of the fraction
1. The original fractions are now equivalent versions of themselves that have the same denominator
2. Now we can just compare the numerators to see which one is bigger
3. 3/8 is now 27/72
4. 4/9 is now 32/72
1. Now we know which of the equivalent fractions is bigger
2. But we want to write the answer in terms of the fractions we started with!
1. 3/8 became the equivalent fraction 27/72
2. 4/9 became the equivalent fraction 32/72
3. 27 is less than 32, so we know that 3/8 is less than 4/9

Compare the fractions 3/8 and 4/9 by finding a common denominator.