Question

Write each of the following ratios in the simplest form:
(i) $Rs6.30:Rs.16.80$
(ii) $3$ weeks $:30$ days
(iii) $3$ m $5$ cm $:35$ cm
(iv) $48$ min $:2$ hours $40$ min
(v) $1$ L $35$ mL $:270$ mL
(vi) $4$ kg $:2$ kg $500$ g

Answer 1

(i) $Rs.6.30:Rs.16.80$

$\frac{6.30}{16.80}=\frac{63}{168}=\frac{63÷21}{168÷21}=\frac{3}{8}$ (H.C.F. of $63$ and $168$ is $21.$)

Ratio in simplest form $=3:8$

(ii) $3$ weeks $:30$ days $=21$ days $:30$ days ($1$ week $=7$ days)

$\frac{21}{30}=\frac{21÷3}{30÷3}=\frac{7}{10}$ (H.C.F. of $21$ and $30$ is $3.$)
Ratio in simplest form $=7:10$

(iii) $3m5cm:35cm=305cm:35cm$ ($1m=100cm$)

$\frac{305}{35}=\frac{305÷5}{35÷5}=\frac{61}{7}$ (H.C.F. of $305$ and $35$ is $5.$)

Ratio in simplest form $=61:7$

(iv) $48$ min $:2$ hours $40$ min $=48$ min $:160$ min ($1$ hour $=60$ mins)

$\frac{48}{160}=\frac{48÷16}{160÷16}=\frac{3}{10}$ (H.C.F. of $48$ and $160$ is $16.$)

Ratio in the simplest form $=3:10$

(v) $1$ L $35$ mL $:270$ mL $=1035$ mL $:270$ mL ($1$ L $=1000$ mL)

$\frac{1035}{270}=\frac{1035÷45}{270÷45}=\frac{23}{6}$ (H.C.F. of $1035$ and $270$ is $45.$)

Ratio in the simplest form $=23:6$

(vi) $4$ kg $:2$ kg $500$ g $=4000$ g $:2500$ g ($1$ kg $=1000$ g)

$\frac{4000}{2500}=\frac{40}{25}=\frac{40÷5}{25÷5}=\frac{8}{5}$ (H.C.F. of $40$ and $25$ is $5.$)

Ratio in the simples form $=8:5$