We have to simplify the ratio 14.4 to 46.4. To simplfy the ratio, cancel out all the common factors in 14.4 and 46.4.
First, we write terms without decimals.
[tex]\begin{gathered} \frac{14.4}{46.4}=\frac{14.4\times10}{46.4\times10}\text{ } \\ =\frac{144}{464} \end{gathered}[/tex]((Multipying numerator and denominator by constant does not change it)
Now, factorise 144 and 464 and cancel common factors.
[tex]\begin{gathered} \frac{144}{464}=\frac{4\times4\times3\times3}{4\times4\times29} \\ =\frac{9}{29} \end{gathered}[/tex]Therefore, simplified ratio is 9 to 29.
