2.01 Name, identify, order, and compare fractions

We've looked at whole numbers, but are all numbers whole?

Part of this shape is shaded and part of it is not. In fact, we can see that the shape is made of five equal parts, and only three of them have been shaded in. We can call this amount $\frac{3}{5}$35​.

The point marked on this number line is halfway between $0$0 and $1$1. That is, the point represents the number that is as far from $0$0 as it is from $1$1. We can call this number $\frac{1}{2}$12​.

These numbers are examples of fractions.

 

Parts of fractions

The top part of a fraction is called the numerator. This tells us how many parts are in the fraction. The bottom part is called the denominator. This tells us how much of a whole each part is. The line in the middle is called the vinculum.

For example, consider $\frac{4}{5}$45​. In this fraction, the numerator is $4$4 and the denominator is $5$5. We can call this fraction $4$4 on $5$5, $4$4 over $5$5, $4$4 out of $5$5, or $4$4 fifths.

 

Improper fractions and mixed numbers

Fractions like $\frac{4}{5}$45​ make up less than a whole. We can tell because the numerator is less than the denominator. We call these proper fractions.

What about a fraction like $\frac{8}{5}$85​? Notice that the numerator is greater than the denominator. This means that the fraction is greater than a whole. We call these improper fractions.

Each row in this grid has been split into five equal parts, and eight parts of the whole have been shaded. We can think about this as eight fifths of one row being shaded. This means that we have a complete row and then three more parts shaded. We can write this number as $1\frac{3}{5}$135​, which we call one and three fifths. We call numbers like this mixed numbers or mixed numerals.

 

Comparing fractions

Exploration

Which fraction is bigger out of $\frac{3}{8}$38​ and $\frac{5}{8}$58​? The first thing we can do is make a visual model for each fraction.

We can see that more of the $\frac{5}{8}$58​ fraction bar has been shaded than the $\frac{3}{8}$38​ fraction bar. Try creating fraction bars for other fractions with a denominator of $8$8. Notice that the smaller the numerator, the smaller the fraction. This works for any two fractions with the same denominator.

Which fraction is bigger out of $\frac{4}{6}$46​ and $\frac{4}{10}$410​? Again, we can make a visual model for each fraction.

Here, more of $\frac{4}{6}$46​ has been shaded than $\frac{4}{10}$410​. Try creating fraction bars for other fractions with a numerator of $4$4. Notice that the smaller the denominator, the bigger the fraction. This works for any two fractions with the same denominator.