Question

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

Answer 1

Answer:

yes

Step-by-step explanation:

Answer 2

Step-by-step 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 ,

$\tt= \dfrac{4}{18}\\\\ = \tt \dfrac{4 \div 2}{18\div 2}\\\\ = \boxed{\orange{\tt \dfrac{2}{9}}}$

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