How can I multiply mixed fractions quickly. On timed tests, I have trouble on problems such as 16$${\frac{{\mathtt{4}}}{{\mathtt{27}}}}$$ * 24$${\frac{{\mathtt{4}}}{{\mathtt{7}}}}$$
+118723 $$\\16\frac{4}{27}\times 24\frac{4}{7}\\\\
=\frac{16*27+4}{27}\times \frac{24*7+4}{7}\\\\
16*27=27*16=20*16+7*16=320+70+42=452\\
7*24=7*20+7*4=140+28=168\\\\
=\frac{456}{27}\times \frac{172}{7}\\\\
4+5+6=15\;$15 is divisable by 3 so 456 is divisable by 3$\\\\
=\frac{456\div 3}{27\div 3}\times \frac{172}{7}\\\\
=\frac{152}{9}\times \frac{172}{7}\\\\
$there are no other common factors so you just have to multiply now and then simplify$$$
So to answer you question - I do not know any really simple way :/
+118723 $$\\16\frac{4}{27}\times 24\frac{4}{7}\\\\
=\frac{16*27+4}{27}\times \frac{24*7+4}{7}\\\\
16*27=27*16=20*16+7*16=320+70+42=452\\
7*24=7*20+7*4=140+28=168\\\\
=\frac{456}{27}\times \frac{172}{7}\\\\
4+5+6=15\;$15 is divisable by 3 so 456 is divisable by 3$\\\\
=\frac{456\div 3}{27\div 3}\times \frac{172}{7}\\\\
=\frac{152}{9}\times \frac{172}{7}\\\\
$there are no other common factors so you just have to multiply now and then simplify$$$
So to answer you question - I do not know any really simple way :/
