Question

Find three different irrational number between the rational numbers 5by7 9by11. Explain it properly. If u had divided show me how u have done

Answer 1

first take the LCM of denominators that is 77.
now if we multiply 11 with 7 and if we multiply 7 with 11 the product is LCM. which ever number the denominator is multiplied. take the same number and multiply with numerator. we are left with 2 rational numbers with the same denominators. see the numerators and select any 3 numbers that fall between the given numbers. don't forget to write the denominators for the selected numbers. the denominators of both the given numbers is 77 (in this case) so the denominators of the selected 3 numbers will also be 77.
$\frac{5}{7} \: and \: \frac{9}{11} \\ lcm = 77 \\ \frac{5 \times 11}{7 \times 11} \: and \: \frac{9 \times 7}{11 \times 7} \\ \frac{55}{77} \: and \: \frac{63}{77} \\ three \: numbers \: between \: \frac{5}{7} \: and \: \frac{9}{11} \: are \\ \frac{57}{77} \: and \: \frac{59}{77} \: and \: \frac{61}{77}$