Question

What is the product of the following fractions: `3/100, 15/49, 7/9`?

Answer 1

`1/140`

Explanation:

A fast way, kind of easy

A calculator might be helpful here.
`3/100\times15/49\times7/9=(3\times15\times7)/(100\times49\times9)=315/44100`

44100`\div`315=140, so`315/44100\times(1/315)/(1/315)`...
`(\cancel(315)^\color(red)(1))/(\cancel(44100)^\color(red)(140))=1/140`

Fastest AND easiest way

`3/15\times15/49\times7/9=(\cancel(3)^(1)\times\cancel(15)^(3)\times\cancel(7)^1)/(\cancel(100)^(20)\times\cancel(49)^(7)\times\cancel(9)^(3))`
`=(1\times\cancel(3)^(1)\times1)/(20\times7\times\cancel(3)^(1))=1/140`