Question

compare the rational number between 10/11and17/18​

Answer 1

Answer:

180/198 is greater than 177 /198 it can be done by taking lcm of denominator and multiplying by numerator

Answer 2

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To compare both the rational numbers,

➡ First find LCM of both denominators. (Least Common Multiple)

➡ LCM of the denominators, 11 and 18, is 198. (Refer to the attachment for Prime Factorisation {LCM})

➡ To make the rational numbers comparable, multiply each rational number, so that, the denominator of both numbers is 198.

➡ $\frac{10}{11} \times \frac{18}{18} = \frac{180}{198} \\ \frac{17}{18} \times \frac{11}{11} = \frac{187}{198}$

➡ Now the numbers are comparable but note, for now, $\frac{10}{11}$ is $\frac{180}{198}$ and $\frac{17}{18}$ is $\frac{187}{198}$.

▶$\frac{180}{198}$ < $\frac{187}{198}$ , So, greater number is $\frac{187}{198}$ that is $\frac{17}{18}$ and smaller is $\frac{180}{198}$ that is $\frac{10}{11}$. $\frac{10}{11}$<$\frac{17}{18}$So we can conclude, $\frac{10}{11}$ is smaller than $\frac{17}{18}$

▶Rational numbers between both are,

$\frac{181}{198}$, $\frac{182}{198}$, $\frac{183}{198}$, $\frac{184}{198}$, $\frac{185}{198}$ and $\frac{186}{198}$. There are 6 rational numbers between $\frac{180}{198}$ and $\frac{187}{198}$.

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What is LCM?

LCM (Least Common multiple is a number which is the smallest number by which two or more numbers are divisible.