Improper Fractions & Mixed Numbers

A-Level Maths Mixed Numbers are called so because they are a mixture of a whole number and a fraction. A whole number is sometimes called an integer.

A-Level Maths Improper fractions are fractions where the number on the top is bigger than the number on the bottom. Improper fractions are also known as top-heavy fractions.

Mixed Numbers and Improper FractionsMixed Numbers and Improper Fractions

Mixed numbers can be expressed as improper fractions and vice versa. Children learn to convert mixed numbers to improper fractions at school at around the age of 9.

Many children struggle to accept the idea of an improper fraction when they first see one and quite often their natural reaction is to turn the fraction upside down so that the larger number is on the bottom. This is because this is what they are used to seeing and that is what they are comfortable with. It will also take some time for them to remember the definitions and you will have to repeat the words ‘mixed numbers’ and ‘improper fractions’ with their definitions a number of times before it sinks in and sticks. In this picture, you can see that one whole and a quarter is the same as five quarters. You can change one and a quarter into five quarters because one whole is the same as four quarters and therefore one whole and a quarter is the same as five quarters. You can also change five quarters into one whole and a quarter by taking four of those quarters and turning into a whole.

 
MixedNumbers2A-Level Maths Understand mixed number & improper fractions in less than 60 seconds… A-Level Maths In the picture on the right, you will see that one whole and two thirds is the same as five thirds. One whole is the same as three thirds and you just need to add on the extra two thirds.

MixedNumbers3The picture on the left is a little more complicated. You will see that two wholes and three fifths is the same as thirteen fifths. Two wholes and three fifths is a mixed number. Thirteen fifths is an improper fraction. Note that one whole is the same as five fifths and so two wholes is the same as ten fifths. Adding on the remaining three fifths gives you the result you see in the picture.