Let's learn a reliable strategy for comparing any two fractions.
Here's our first comparison. Which is greater, 5 9ths or 2/3? By looking at the total shaded area of each fraction, we can see that 2/3 is greater than 5 9ths. Let's try another one. Which is greater, 5/8 or 3/4s? There seems to be more unshaded parts in 5/8 than 3/4s.
However, the visual models here are harder to compare directly.
When it's not visually obvious, we can use equivalent fractions to find a common denominator. This means we can rewrite one or both fractions so they have the same number of total parts.
Let's compare 5/8 and 3/4s again. The denominators are 8 and 4.
Since 4 goes into 8, let's turn the fourths into 8. We multiply the numerator and denominator of 3/4s by 2.
3 * 2 = 6 and 4 * 2 = 8. So 3/4 is equivalent to 68.
Now the comparison is simple. Which is greater? 5/8 or 6? Since 6 is more than 5, 6 is greater. That means 3/4 is the greater fraction.
Let's apply this to another example. 5 12ths and 1/3. The denominators are 12 and 3. We can turn/3 into 12ths. We multiply the top and bottom of 1/3 by 4.
1 * 4 = 4 and 3 * 4 = 12. So 1/3 is the same as 4 12ths. Now we can easily compare 5 12ths and 4 12ths. 5 is greater than 4. So 5 12ths is the larger fraction.
How about 116 and 68? Let's find a common denominator. We can change 8 into 16 by multiplying by 2. 6 * 2 = 12 and 8 * 2 = 16. So 68 is equivalent to 126.
Comparing 1116 to 1216, we can see that 1216 is greater, which means 68 is greater than 116.
We can also compare fractions without using visuals. We can change 56 into 12ths by multiplying the numerator and denominator by 2. 5 * 2 is 10 and 6 * 2 is 12. So 56 is equivalent to 10 12ths.
11 12ths is larger than 10 12ths.
The key takeaway is that we can create equivalent fractions to make comparisons easier. By turning 6/8 into 126, we could compare it to 1116. Making the denominators match lets us compare the number of parts directly.
