Question

Subtract:

(i) $\frac{2}{7}\mathrm{from}\frac{19}{21}$
(ii) $\frac{21}{25}\mathrm{from}\frac{18}{20}$
(iii) $\frac{7}{16}\mathrm{from}2$
(iv) $\frac{4}{15}\mathrm{from}2\frac{1}{5}$

Answer 1

(i)
$$\begin{gathered} \frac{19}{21}-\frac{2}{7} \\ \mathrm{LCM}\mathrm{of}21\&7\mathrm{is}21,\mathrm{so}\mathrm{we}\mathrm{convert}\mathrm{each}\mathrm{fraction}\mathrm{into}\mathrm{an}\mathrm{equivalent}\mathrm{fraction}\mathrm{with}\mathrm{denominator}21. \\ =\frac{19\times 1}{21\times 1}-\frac{2\times 3}{7\times 3}=\frac{19}{21}-\frac{6}{21} \\ =\frac{19-6}{21}=\frac{13}{21} \end{gathered}$$

(ii)
$$\begin{gathered} \frac{18}{20}-\frac{21}{25} \\ \mathrm{LCM}\mathrm{of}20\&25\mathrm{is}100,\mathrm{so}\mathrm{we}\mathrm{convert}\mathrm{each}\mathrm{fraction}\mathrm{into}\mathrm{an}\mathrm{equivalent}\mathrm{fraction}\mathrm{with}\mathrm{denominator}100. \\ =\frac{18\times 5}{20\times 5}-\frac{21\times 4}{25\times 4}=\frac{90}{100}-\frac{84}{100} \\ =\frac{6}{100} \end{gathered}$$

(iii)
$$\begin{gathered} \frac{2}{1}-\frac{7}{16} \\ \mathrm{LCM}\mathrm{of}1\&16\mathrm{is}16,\mathrm{so}\mathrm{we}\mathrm{convert}\mathrm{each}\mathrm{fraction}\mathrm{into}\mathrm{an}\mathrm{equivalent}\mathrm{fraction}\mathrm{with}\mathrm{denominator}16. \\ =\frac{2\times 16}{1\times 16}-\frac{7\times 1}{16\times 1}=\frac{32}{16}-\frac{7}{16} \\ =\frac{32-7}{16} \\ =\frac{25}{16} \end{gathered}$$

(iv)
$$\begin{gathered} 2\frac{1}{5}-\frac{4}{15}=\frac{(5\times 2)+1}{5}-\frac{4}{15} \\ =\frac{11}{5}-\frac{4}{15} \\ \mathrm{LCM}\mathrm{of}5\&15\mathrm{is}15,\mathrm{so}\mathrm{we}\mathrm{convert}\mathrm{each}\mathrm{fraction}\mathrm{into}\mathrm{an}\mathrm{equivalent}\mathrm{fraction}\mathrm{with}\mathrm{denominator}15. \\ \frac{11\times 3}{5\times 3}-\frac{4\times 1}{15\times 1} \\ \frac{33}{15}-\frac{4}{15}=\frac{33-4}{15} \\ =\frac{29}{15} \end{gathered}$$