FRACTIONS - Basic Operations

Addition/Subtraction

${2\over 7}+{3\over 7}={2+3\over 7}={5\over 7}$

 ${7\over 10}-{4\over 10}={7-4\over 10}={3\over 10}$

${1\over 4}+{2\over 5}$

$={1\times 5\over 4\times 5}+{2\times 4\over 5\times 4}$

$={5\over 20}+{8\over 20}$

$={13\over 20}$

Multiplication

 ${4\over 5}\times{5\over 6}={4\times 5\over 5\times 6}={20\over 30}={2\over 3}$

Division

 ${4\over 5}\div{5\over 6}=
{4\over 5}\times{6\over 5}={4\times 6\over 5\times 5}={24\over 25}$

'Over'
${{2\over 5}\over 6} ={2\over 5}\div 6={2\over 5} \times {1\over 6}={2\over 30}={1\over 15}$

${2\over {5\over 6}} =2\div {5\over 6}=2\times {6\over 5}={12\over 5}=2 {2\over 5}$

${{a\over b}\over c} ={a\over bc}$

${a\over {b\over c}}={ac\over b}$