Simplify ratio 152:121.6:212.8

Question

How am I supposed to know that I can simplify the ratio by dividing with 30.4? Is that such an obvious common factor? How would you go about this if you had 60 seconds time to solve it?

You're supposed to arrive at 5:4:7.

Answer 1

Take $152:121.6:212.8$

Multiply by five to remove decimals: $760:608:1064$

Take out a multiple of $2^3=8$ to get $95:76:133$

$95=5\times 19$ is an obvious factorisation. $5$ is clearly not a common factor. $19$ turns out to be, and gives $$5:4:7$$

Answer 2

I would do $$ \frac{152}{121.6}=1.25=\frac54, \ \ \frac{121.6}{212.8}=0.\overline{5714285}=\frac{571428}{999999}=\frac47. $$

Or if you cannot recognize the second fraction right away, $$ \frac{121.6}{212.8}=\frac{1216}{2128}=\frac{64\times19}{16\times133}=\frac{64\times19}{16\times7\times19}=\frac47. $$