Number Theory

Fractions

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

$2842=2×143×14 =23$ $4.510.5=45105 =3×157×15=37$

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.
$325=12100=0.12$ $720=7×100%20 =7×5%=35%$

Directed Number

$3+4=7$ $3-4=-1$ $3+-4=3-4=-1$ $3--4=3+4=7$ $-3+4=1$ $-3+-4=-3-4=-7$ $-3×-4=12$

Order of Operation

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

BIDMAS

Brackets - Indices - Division and/orMultiplication - Addition and/orSubtraction

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

Sequences& Series

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

$3×3×3×3=34$

Indices is the plural of index

The laws of indices

Some powers of 10 have a name called a prefix.

PrefixLetterPowerNumber
teraT10121,000,000,000,000
gigaG1091,000,000,000
megaM1061,000,000
kilok1031,000
decid10-10.1
centic10-20.01
millim10-30.001
microμ10-60.000 001
nanon10-90.000 000 001
picop10-120.000 000 000 001

Prime Factorization

Units & Prefixes
SI (or "Systeme Internationale d'Unites")
SI Prefixes
SI is Not the Only Measurement System