Question

insert three rational numbers between 1/3 and 5/9

Answer 1

Hi.

$\text{To insert 3 rationals between \dfrac{1}{3} and \dfrac{5}{9} }\\\\\\\text{First, take their LCM.}\\\\\text{LCM of \dfrac{1}{3} and \dfrac{5}{9} = \dfrac{3}{9} and \dfrac{5}{9} }\\\\\\\text{Now, if we need to find 3 rational numbers, multiply both the fractions by \dfrac{4}{4} }\\\\\\\dfrac{3 \times 4}{9 \times 4} \: and \: \dfrac{5 \times 4}{9 \times 4}\\\\\\or \: \dfrac{12}{36} \: and \: \dfrac{20}{36}$

$\text{Thus, 3 rational numbers between} \dfrac{12}{36} \: and \: \dfrac{20}{36} \: \text{or \dfrac{1}{3} and \dfrac{5}{9} }\\\\\\\text{Are} \: \dfrac{13}{36}, \: \dfrac{14}{36}, \: \dfrac{15}{36} \: and \: so \: on...$

Hope it helps.