We've looked at whole numbers, but are all numbers whole?
These numbers are examples 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.
What fraction of the hexagon below is shaded?
A fraction is a number which can be made of equal parts of a whole number.
A fraction is made up of:
A top number called the numerator which says how many equal parts are in the fraction
A bottom number called the denominator which says how much of a whole each part is
A line between the two numbers called the vinculum
Fractions like \dfrac{4}{5} 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 \dfrac{8}{5}? Notice that the numerator is greater than the denominator. This means that the fraction is greater than a whole. We call these improper fractions.
We can write this number as 1\,\dfrac{3}{5}, which we call one and three fifths.
We call numbers like this mixed numbers or mixed numerals.
What number is plotted on the number line? Give your answer as a mixed number.
Fractions where the numerator is less than the denominator are called proper fractions. Fractions where the numerator is more than the denominator are called improper fractions.
Numbers which are made up of a whole number and a fraction are called mixed numbers or mixed numerals.
Which fraction is bigger out of \dfrac{3}{8} and \dfrac{5}{8}? The first thing we can do is make a visual model for each fraction.
We can see that more of the \dfrac{5}{8} fraction bar has been shaded than the \dfrac{3}{8} fraction bar. Try creating fraction bars for other fractions with a denominator of 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 \dfrac{4}{6} and \dfrac{4}{10}? Again, we can make a visual model for each fraction.
Here, more of \dfrac{4}{6} and has been shaded than \dfrac{4}{10}. Try creating fraction bars for other fractions with a numerator of 4. Notice that the smaller the denominator, the bigger the fraction. This works for any two fractions with the same denominator.
Use the following applet to practise comparing fractions. Sort the fractions by dragging them until they are inside the black boxes.
Fraction bars can help us compare fractions.
Which inequality symbol completes the sentence: \dfrac{1}{5} ⬚ \dfrac{1}{6}?
Fraction bars can help us compare fractions.
For any two fractions with the same denominator: the smaller the numerator, the smaller the fraction.
For any two fractions with the same numerator: the larger the denominator, the smaller the fraction.