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Mathematics Question on Need For Rational Numbers

List five rational numbers between:
(i) –1 and 0
(ii) –2 and –1
(iii)−45  and−23\frac{-4}{5} \space and \frac{-2}{3}

(iv) −12  and23\frac{-1}{2}\space and \frac{2}{3}

Answer

(i) –1 and 0
= −110,−120,−130,−140,−150\frac{-1}{10},\frac{-1}{20},\frac{-1}{30},\frac{-1}{40},\frac{-1}{50}

(ii) –2 and –1
=−2=−126  and= -2 = \frac{-12}{6} \space and

=−1=−66= -1 = \frac{-6}{6}

Five rational numbers are
= −116,−106,−96,−86,−76\frac{-11}{6},\frac{-10}{6},\frac{-9}{6},\frac{-8}{6},\frac{-7}{6}

(iii)−45  and−23\frac{-4}{5}\space and \frac{-2}{3}

= −45\frac{-4}{5}

= −4×95×9\frac{-4\times9}{5\times9}

= −3645  and\frac{-36}{45}\space and

= −23=−2×153×15\frac{-2}{3}= \frac{-2\times15}{3\times15}

= −3045\frac{-30}{45}

Five rational numbers are
= −3545,−3445,−3345,−3245,−3145\frac{-35}{45},\frac{-34}{45},\frac{-33}{45},\frac{-32}{45},\frac{-31}{45}

(iv) −12  and23\frac{-1}{2} \space and \frac{2}{3}

= 12=1×182×18\frac{1}{2}=\frac{1\times18}{2\times18}

= 1836\frac{18}{36} and

23=2×123×12\frac{2}{3}=\frac{2\times12}{3\times12}

= 2436\frac{24}{36}
Five rational numbers are

= 1936,2036,2136,2236,2336\frac{19}{36},\frac{20}{36},\frac{21}{36},\frac{22}{36},\frac{23}{36}