Question

find 6 rational numbers
by multiply
3/7 and 8/9
​

Answer 1

Finding rational number between ☞

$\red{\bigg( \bf \large \frac{3}{7} \bigg) \bf \: {and} \: \bigg( \large \frac{8}{9} \bigg)}$

LCM of denominator = 63 [ As 7 & 9 are multiplied because no digit can divide both 7 & 9 in one time ]

Now,

Making the denominator same of both fractions.

$\implies \: \sf \large \frac{3 \times 9}{7 \times 9} = \frac{27}{63}$

$\implies \: \sf \large \: \frac{8 \times 7}{9 \times 7} = \frac{56 }{63}$

Now , finding 6 rational number between the fraction er get.

$\large\green{\frac{27}{63} \bigg(\: \frac{28}{63} , \: \frac{29}{63}, \: \frac{30}{63}, \: \frac{31}{63} , \: \frac{32}{63}, \: \frac{33}{63} \bigg)\frac{56}{63}}$

So,

The 6 rational numbers are , $\large\purple{ \frac{28}{63} , \: \frac{29}{63}, \: \frac{30}{63}, \: \frac{31}{63} , \: \frac{32}{63} \: \& \: \frac{33}{63}}$

There are many more methods to solve this type of ques.

Additional information :-

Here are two more methods to do this :-

$\huge\green \maltese$

$\large \rm \: d = \frac{b - a}{n + 1} \\ \\ \sf \: first \: rational \: no. \: = \red{a + d} \\ \\ \sf \: second \: rational \: no. \: = \red{a + 2d}$

$\huge\green \maltese$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \small \frac{1}{2}\bigg( a + b \bigg) = 1st \: Rational \: number \\ \bf Again , \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \small\frac{1}{2}\bigg( a + b \bigg) = 2nd \: Rational \: number$

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$\large\underline\mathcal\pink {Hope \: This \: Helps \: You}$