Comparisons using models
You may have already learned about fractions as areas of shapes.
The denominator (bottom number) of a fraction shows us a number of equal size pieces the will make a whole. For example, thirds means three equal size pieces will make a whole.
The numerator (top number) shows the number of parts selected, which makes up the value of the fraction.
Comparing the size of fractions
When the fractions have the same size pieces (i.e. the same denominators), we can compare their size simply by looking at how many pieces are in the fraction (ie. the numerators). Let's watch a video to see how we can use area models to help us do this.
Example
Question 1:
Which fraction is larger?
$\frac{1}{5}$15 A
$\frac{2}{5}$25 B
Complements to one whole
The numerators of fractions are showing a number of parts and the denominators are showing the size of those parts. The denominator also shows us how many parts make one whole. If we want to know how many more parts to make one whole, we add the number of pieces to make up one whole.
Watch this video to learn about component parts of fractions to make one whole.
Example
Question 2:
If I have 1 fourth, how many more fourths do I need to make a whole?
When comparing fractions, if the denominators are the same, then we can compare the numerators.
The denominator also tells us how many parts make up one whole.