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Mathematics Question on Need For Rational Numbers

Write the following rational numbers in ascending order:
(i) -35\frac{3}{5},-25\frac{2}{5},-15\frac{1}{5}
(ii) -13\frac{1}{3},-29\frac{2}{9},-43\frac{4}{3}
(iii) -37\frac{3}{7},-32\frac{3}{2},-34\frac{3}{4}

Answer

(i) -35\frac{3}{5},-25\frac{2}{5},-15\frac{1}{5}
As -3 < -2 < -1,
∴ -35\frac{3}{5}<-25\frac{2}{5}<-15\frac{1}{5}

(ii) -13\frac{1}{3},-29\frac{2}{9},-43\frac{4}{3}
By converting these into like fractions,
−1×33×3\frac{-1\times 3}{3\times3}, -29\frac{2}{9}, -4×33×3\frac{4\times 3}{3\times 3}
-39\frac{3}{9}, -29\frac{2}{9}, -129\frac{12}{9}
As -12<-3<-2
∴ -43\frac{4}{3}<-13\frac{1}{3}<-29\frac{2}{9}

(iii) -37\frac{3}{7},-32\frac{3}{2},-34\frac{3}{4}
By converting these into like fractions,
-1248\frac{12}{48}, -4228\frac{42}{28}, -2128\frac{21}{28}
As - 42 < - 21 < - 12,
∴ -32\frac{3}{2} < -34\frac{3}{4} < -37\frac{3}{7}