Solveeit Logo
Login

Question

Mathematics Question on Need For Rational Numbers

Give four rational numbers equivalent to:
(i)−27\frac{-2}{7}
(ii) 5−3\frac{5}{-3}
(iii) 49\frac{4}{9}

Answer

(i) −27\frac{-2}{7}
Four rational numbers are
=−2×27×2,−2×37×3,−2×47×4,−2×57×5=\frac{-2\times2}{7\times2},\frac{-2\times3}{7\times3},\frac{-2\times4}{7\times4},\frac{-2\times5}{7\times5}

=−414,−621,−828,−1035=\frac{-4}{14},\frac{-6}{21},\frac{-8}{28},\frac{-10}{35}

(ii) 5−3\frac{5}{-3}
Four rational numbers are
=5×2−3×2,5×3−3×3,5×4−3×4,5×5−3×5=\frac{5\times2}{-3\times2},\frac{5\times3}{-3\times3},\frac{5\times4}{-3\times4},\frac{5\times5}{-3\times5}

=10−6,15−9,20−12,25−15=\frac{10}{-6},\frac{15}{-9},\frac{20}{-12},\frac{25}{-15}

(iii)49\frac{4}{9}
Four rational numbers are
=4×29×2,4×39×3,4×49×4,4×59×5=\frac{4\times2}{9\times2},\frac{4\times3}{9\times3},\frac{4\times4}{9\times4},\frac{4\times5}{9\times5}

=818,1227,1636,2045=\frac{8}{18},\frac{12}{27},\frac{16}{36},\frac{20}{45}