Question

rational number between 3 upon 5 and 1​

Answer 1

${ \huge{ \bf{ \underline{Question}}}}$

$\sf{find \: a \: rational \: number \: between \: \frac{3}{5} and \: 1}$

${ \huge{ \bf{ \underline{Answer}}}}$

Before we find the rational numbers between 3/5 and 1 ; let us learn what are rational numbers .

What are rational numbers ?

Rational numbers are the numbers which can be expressed in p/q form where p and q are integers and q is not equal to 0.

How do we find more rational numbers between the rational numbers given ?

Step 1 : Check if the denominators of the given rationals are same. If not ; make them same by taking their LCM .

Step 2 : Multiply both the sides of the rationals by a common number .

For Example :

Let us consider the rationals :

$\frac{2}{3} and \frac{5}{3}$

$now \: we \: will \: multiply \: them \: both \: with \: a \: common\\ \: number \: 10 \: for \: example. \\ \frac{2 \times 10}{3 \times 10} = \frac{20}{30} \\ \frac{5 \times 10}{3 \times 10} = \frac{50}{30}$

Step 3 : After we obtain rationals with same denominators and after Multiplying by common number ; we will get many rational numbers between the given rationals.

Following the above steps we will solve the given Question.

${ \huge{ \bf{ \underline{Solution}}}}$

$\frac{3}{5} and \frac{1}{1} as \: 1 \: can \: be \: written \: as \: 1 \: by \: 1 \\ \\ \\ lcm = 5 \\ \frac{3 \times 1}{5 \times 1 } = \frac{3}{5} \\ \\ \\\frac{1 \times 5}{1 \times 5} = \frac{5}{5} \\ \\ \\ = \frac{4}{5} lies \: between \: \frac{3}{5} and \: 1 \\ \\ \\ if \: we \: want \: more \: rationals = \\ \\ \frac{3 \times 10}{5 \times 10} = \frac{30}{50} and \frac{5 \times 10}{5 \times 10} = \frac{50}{50} \\ \\ we \: can \: pick \: many \: rationals \: between\\ \: \frac{30}{50} and \frac{50}{50}$