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Question

1. Five rational numbers between $$2$$ and $$1$$ are
2. Four rational numbers between $$\dfrac{2} {3}$$ and $$\dfrac{3} {5}$$ are


Solution

(i) as we have to five rational number ,we multiply  number by $$\dfrac66$$
i.e 
$$1\times\dfrac66= \dfrac66 $$ and $$2\times\dfrac66=\dfrac{12}{6}$$
thus 5 rational number between 1and 2 are $$\dfrac76,\dfrac86,\dfrac96,\dfrac{10}{6},\dfrac{11}{6}$$

(ii) as in $$\dfrac23 ,\dfrac35$$ isn't denominator same , to make same denominator take LCM of 3 and 5

i.e LCM(3,5)= 15

now,

fractions are $$\dfrac{10}{15}$$ and $$\dfrac{9}{15}$$

multiply $$\dfrac{10}{15}$$ and $$\dfrac{9}{15} $$ by $$\dfrac55$$

$$\Rightarrow\dfrac{50}{75},\dfrac{45}{75}$$

thus 4 rational number between $$\dfrac{2}{3}$$and $$\dfrac35$$ are $$\dfrac{46}{75},\dfrac{47}{75},\dfrac{48}{75},\dfrac{49}{75}$$

Mathematics

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