Comparisons using models
You may have already learned about fractions as areas of shapes.
We know that fractions show a number of equal size pieces (denominator) of a whole. For example, eighths are showing a number where eight equal size pieces will make a whole.
The number of parts selected (numerator) shows the value of the fraction.
Comparing the size of fractions
We can compare the size of fractions by looking at each of the fractions as an area of the same shape. Watch this video to learn about comparing fractions using area models.
When the fractions have the same size pieces (i.e. the same denominator), we can compare their size simply by looking at how many pieces are in the fraction (numerator).
Worked Examples
Question 1
Which fraction is smaller?
$\frac{2}{6}$26 A
$\frac{3}{6}$36 B
QUESTION 2
Which fraction is larger?
$\frac{1}{10}$110 A
$\frac{2}{10}$210 B
Complements to one whole
The denominator of a fraction also shows how many parts make one whole. If we want to know how many more parts 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.
Another Worked Example
question 3
If I have 1 sixth, how many more sixths do I need to make a whole?
When comparing fractions, if the denominator is the same, then we compare the numerator.
The denominator tells us how many parts make up one whole.