## Fractions

A fraction has been simplified when the numerator and the denominator have no common factor greater than one.

$$\frac{28}{42}=\frac{2\times 14}{3\times 14}=\frac{2}{3}$$ $$\frac{4.5}{10.5}=\frac{45}{105}=\frac{3\times 15}{7\times 15}=\frac{3}{7}$$### Remember

- to write a fraction as a decimal, divide the numerator by the demoninator;
- to change a fraction, or a decimal, into a percentage, multiply by 100;
- to change a percentage into a fraction, rewrite % as divided by 100.

## Directed Number

$$3+4=7$$ $$3-4=-1$$ $$3+-4=3-4=-1$$ $$3--4=3+4=7$$ $$-3+4=1$$ $$-3+-4=-3-4=-7$$ $$-3\times -4=12$$## Order of Operation

The order in which operations are performed can be remember by the mnemonic

## BIDMAS

###
**B**rackets -
**I**ndices -
**D**ivision and/or
**M**ultiplication -
**A**ddition and/or
**S**ubtraction

This will help in remembering the correct priority of operations when completing calculations. Those on the lelf have priority over those on the right.

In index notation, the number being multiplied by itself is called the base. The number written above the base is called the index or power or order.

For example: if the base is 3 and the index is 4 then

Indices is the plural of index

## The laws of indices

Some powers of 10 have a name called a prefix.

Prefix | Letter | Power | Number |
---|---|---|---|

tera | T | 10^{12} | 1,000,000,000,000 |

giga | G | 10^{9} | 1,000,000,000 |

mega | M | 10^{6} | 1,000,000 |

kilo | k | 10^{3} | 1,000 |

deci | d | 10^{-1} | 0.1 |

centi | c | 10^{-2} | 0.01 |

milli | m | 10^{-3} | 0.001 |

micro | μ | 10^{-6} | 0.000 001 |

nano | n | 10^{-9} | 0.000 000 001 |

pico | p | 10^{-12} | 0.000 000 000 001 |