## 2. Fractions, and adding and subtracting fractions

A fraction is simply one number divided by another, for instance ¾ is 3 (called the numerator) divided by 4 (called the denominator).

3 | = 3 ÷ 4 |

4 |

If the numerator is equal to the denominator, the fraction has the exact value of one. If the numerator is larger than the denominator, the fraction is termed an improper fraction, and it can be expressed as a whole number and a proper fraction. For instance:

11 | = 2 | 3 |

4 | 4 |

where 4 divided into 11 gives 2, leaving a remainder of 3. Similarly, if we have a mixed number, we can express this as an improper fraction:

5 | 1 | = | 21 |

4 | 4 |

where 5 is multiplied by 4 (the denominator) to give 20, and then the extra ¼ is added to give 21. The logic of this process will (should, may) become clearer when we look at adding fractions together.