Question

Are the ratios 4:18 and 2:9 equivalent?
yes
no

Answer 1

yes

Explanation:

Answer 2

Explanation:

Two ratios are given to us and we need to tell whether they are equivalent or not . Firstly let us say we have two ratios q:p and r:s . Here p & q are co-primes and r & s are also co-primes. Then the two ratios will be equal if and only if

• q = r
• p = s .

Theefore , the Ratios are ,

`\begin{cases}\tt 4 : 18 \\\tt 2:9 \end{cases}`

Here we see that the ratio 2:9 is in simplest form that is HCF of 2 & 9 is 1 . But here 4:18 is not in simplest form . HCF of 4 & 18 is not 1 it's 2 .On dividing numerator and denominator by 2 , we have ,

`\tt= (4)/(18)\\\\ = \tt (4 / 2)/(18/ 2)\\\\ = \boxed{\orange{\tt (2)/(9)}}`

Therefore since the Ratios are equal in the simplest form . Therefore the Ratios are equal.