Let's compare fractions visually. We can imagine the vertical lines continuing in the shape on the left. So it can be divided into nine equal parts with five parts shaded. The shape on the right is divided into nine equal parts with four shaded.
5 9ths is larger than 4 9ths. So the shape on the left is greater.
Let's try another pair. If we imagine adding a horizontal and vertical line in the middle of the shape on the left, it would have eight equal triangles with three of them shaded. The second shape is divided into eight equal parts with four shaded. Since 48 is greater than 3/8, the shape on the right represents the larger fraction.
Since these shapes had the same denominator, we could just compare how many parts were shaded.
Here the shape on the left can be divided into 12 equal parts by dividing each column into four.
Then there are four out of 12 parts shaded. The shape on the right has 12 equal parts with three parts shaded. So 4 12ths is greater than 3 12ths. Let's look at a different problem.
We can divide both shapes into 16 equal parts. The shape on the left has five out of 16 parts shaded. So it represents 516.
The shape on the right has six parts shaded representing 66.
Because the denominators are both 16, we just compare the numerators.
6 is greater than 5, which means 616 is the larger fraction.
This rule works even without visualizations.
Let's compare 81 and 71. They have the same denominator, 11. This tells us the size of the pieces is the same for both fractions. We just need to see which fraction has more of those pieces. 8 is more than seven. So 8 11ths is the greater fraction.
When denominators are the same, the fraction with the larger numerator is always greater. For example, with 516 and 616, we know they're both divided into 16 parts. We just compare the numerators 5 and 6 to see that 616 is greater.
