Question

Express each of the following ratios in the simplest form:
(i) $36:90$
(ii) $324:144$
(iii) $85:561$
(iv) $480:384$
(v) $186:403$
(vi) $777:1147$

Answer 1

(i) Given $36:90=\frac{36}{90}$
Since, HCF of $36=18\times 2$ and $90=18\times 5$ is $18$
So, $\frac{36÷18}{90÷18}=\frac{2}{5}$
Since, the H.C.F. of $2$ and $5$ is $1$.
Thus, the simplest form of $36:90$ is $2:5$.
(ii) Given $324:144=\frac{324}{144}$
Since, HCF of $324=6\times 6\times 9$ and $144=6\times 6\times 4$ is $36$
So, $\frac{324÷36}{144÷36}=\frac{9}{4}$
Since the H.C.F. of $9$ and $4$ is $1$,
Thus, the simplest form of $324:144$ is $9:4$.
(iii) Given$85:561=\frac{85}{561}$
Since, the H.C.F. of $85=17\times 5$ and $561=17\times 11\times 3$ is $17$
So, $\frac{85÷17}{561÷17}=\frac{5}{33}$
Since the H.C.F. of $5$ and $33$ is $1$,
Thus, the simplest form of $85:561$ is $5:33$.
(iv) Given $480:384=\frac{480}{384}$
Since, the H.C.F. of $480=96\times 5$ and $384=96\times 4$ is $96$
So, $\frac{480÷96}{384÷96}=\frac{5}{4}$
Since, the H.C.F. of $5$ and $4$ is $1$.
Thus, the simplest form of $480:384$ is $5:4$.
(v) Given $186:403=\frac{186}{403}$
The H.C.F. of $186=6\times 31$ and $403=13\times 31$ is $31$
So, $\frac{186÷31}{403÷31}=\frac{6}{13}$
Since the H.C.F. of $6$ and $13$ is $1$,
Thus, the simplest form of $186:403$ is $6:13$.
(vi) Given $777:1147=\frac{777}{1147}$
Since, HCF of $777=37\times 21$ and $1147=37\times 31$ is $37$.
So, $\frac{777÷37}{1147÷37}=\frac{21}{31}$
Since, the H.C.F. of $21$ and $31$ is $1$,
Thus, the simplest form of $777:1147$ is $21:31$.