Answer:
\(\text{(A) Hence, The ratio }\frac{10}{20}\text{ form a proportion by common multiplier 3 to get }\frac{30}{60}\)
\(\text{(B) Hence, Both ratio are equal to }\frac{1}{2}\text{ in simplest form. }\)
Step-by-step explanation:
(A) We need to show both fraction of same proportion.
Ratio 1: \(\frac{10}{20}\)
If we multiply by 3 at numerator and denominator
\(\RIghtarrow \frac{10\times 3}{20\times 3}\)
\(\RIghtarrow \frac{30}{60}\)
\(\RIghtarrow \frac{30}{60} \text{ is equivalent ratio of second one }\frec{30}{60}\)
\(\text{Hence, The ratio }\frac{10}{20}\text{ form a proportion by common multiplier 3 to get }\frac{30}{60}\)
(B) Now we simplify both ration into simplest form
\(\Rightarrow \frac{10\div 10}{20\div 10}=\frac{1}{2}\)
\(\Rightarrow \frac{30\div 30}{60\div 30}=\frac{1}{2}\)
\(\Rightarrow \frac{1}{2}=\frac{1}{2}\)
\(\text{Hence, Both ratio are equal to }\frac{1}{2}\text{ in simplest form. }\)
