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How do you evaluate $\dfrac{4r}{s}$ if $r=9$ and $s=2$?

seo-qna
Last updated date: 19th Jun 2024
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Answer
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Hint: We first try to describe the relation between the denominator and the numerator to find the simplified form. We complete the multiplication in the numerator part. We use the G.C.D of the denominator and the numerator to divide both of them. We get the simplified form when the denominator is 1.

Complete step-by-step solution:
We need to find the simplified form of $\dfrac{4r}{s}$ if $r=9$ and $s=2$.
We first place the value in the expression of $\dfrac{4r}{s}$.
We get $\dfrac{4r}{s}=\dfrac{4\times 9}{2}$.we get the multiplied value of $4\times 9=36$ in the numerator.
Now we need to find the simplified form of the division of $\dfrac{36}{2}$.
Simplified form is achieved when the G.C.D of the denominator and the numerator is 1.
For any fraction $\dfrac{p}{q}$, we first find the G.C.D of the denominator and the numerator. If it’s 1 then it’s already in its simplified form and if the G.C.D of the denominator and the numerator is any other number d then we need to divide the denominator and the numerator with d and get the simplified fraction form as $\dfrac{{}^{p}/{}_{d}}{{}^{q}/{}_{d}}$.
For our given fraction $\dfrac{36}{2}$, the G.C.D of the denominator and the numerator is 2.
Now we divide both the denominator and the numerator with 2 and get $\dfrac{{}^{36}/{}_{2}}{{}^{2}/{}_{2}}=\dfrac{18}{1}=18$.
Therefore, the value of $\dfrac{4r}{s}$ for $r=9$ and $s=2$ is 18.

Note: The process is similar if we complete the division part first. We take the division of $\dfrac{4}{2}$ which gives $\dfrac{4}{2}=2$. Then we multiply the quotient with 9 to get $2\times 9=18$. Change of operations doesn’t affect the final result.