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If you get Equation: {7} out of Equation: {10} in a test, you can write your score as Equation: frac{7}{10}.

Equation: {7} expressed as a fraction of Equation: {10} is Equation: frac{7}{10}.

Similarly, if there are Equation: {20} socks in a drawer and Equation: {4} of them are blue, Equation: frac{4}{20}of the socks are blue.

Equation: {4} expressed as a fraction of Equation: {20} is Equation: frac{4}{20}. We can put this into its simplest form by dividing the top and bottom numbers by Equation: {4}, so we get Equation: frac{1}{5}.

Fractions can be illustrated by dividing a shape into equal parts, and shading a certain number of these parts. The bottom number is the number of equal parts that diagram has been cut into, and the top number is the number of equal parts that has been shaded.

Cutting the cake into six equal pieces and eating two is equivalent to cutting the cake into three equal pieces and eating one. You eat the same amount of cake in both cases.

When writing equivalent fractions, do the same multiplication or division to the top and bottom numbers. For example, if you multiply the top by 2, you must also multiply the bottom by 2.

You know that: Equation: frac{4}{12} = frac{2}{6} = frac{1}{3}

Equation: {4} and Equation: {12} have a common factor, namely Equation: {4}, so Equation: frac{4}{12} can be written as Equation: frac{1}{3} (divide the top and the bottom by Equation: 4).

Equation: {2} and Equation: {6} have a common factor, namely Equation: {2}, so Equation: frac{2}{6} can be written as Equation: frac{1}{3}(divide the top and the bottom by Equation: {2}).

However, Equation: {1} and Equation: {3} have no common factors, so Equation: frac{1}{3} cannot be simplified. When a fraction cannot be simplified we say that it is its simplest form.

A whole number can be written as Equation: frac{2}{2}Equation: frac{3}{3}Equation: frac{4}{4}, etc.

So Equation: 1 frac{2}{3} can be written as:

Equation: frac{3}{3} + frac{2}{3} = frac{5}{3}

Mixed numbers

Equation: 1frac{2}{3} is known as a mixed number, because it is made up of a whole number and a fraction.

Improper fractions

Equation: frac{5}{3} is called an improper fraction, because the top number is bigger than the bottom number.

Converting from a mixed number to an improper


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