\displaystyle \textbf{Question 1: }\text{Add:}
\displaystyle \text{(i) }\frac{16}{21}+\frac{23}{28}\qquad\text{(ii) }6\frac{7}{12}+4\frac{7}{18}
\displaystyle \text{(iii) }9\frac{3}{4}+7\frac{7}{8}+3\frac{5}{12}
\displaystyle \text{Answer:}
\displaystyle \text{(i) }\frac{16}{21}+\frac{23}{28}
\displaystyle \text{L.C.M. of }21\text{ and }28=84.
\displaystyle =\frac{64}{84}+\frac{69}{84}=\frac{133}{84}=1\frac{49}{84}=1\frac{7}{12}.

\displaystyle \text{(ii) }6\frac{7}{12}+4\frac{7}{18}=\frac{79}{12}+\frac{79}{18}
\displaystyle \text{L.C.M. of }12\text{ and }18=36.
\displaystyle =\frac{237}{36}+\frac{158}{36}=\frac{395}{36}=10\frac{35}{36}.

\displaystyle \text{(iii) }9\frac{3}{4}+7\frac{7}{8}+3\frac{5}{12}=\frac{39}{4}+\frac{63}{8}+\frac{41}{12}
\displaystyle \text{L.C.M. of }4,\ 8,\ 12=24.
\displaystyle =\frac{234}{24}+\frac{189}{24}+\frac{82}{24}
\displaystyle =\frac{505}{24}=21\frac{1}{24}.

\displaystyle \\

\displaystyle \textbf{Question 2: }\text{Subtract:}
\displaystyle \text{(i) }\frac{9}{10}-\frac{7}{15}\qquad\text{(ii) }13-6\frac{2}{5}\qquad\text{(iii) }2\frac{13}{35}-1\frac{7}{30}
\displaystyle \text{Answer:}
\displaystyle \text{(i) }\frac{9}{10}-\frac{7}{15}
\displaystyle \text{L.C.M. of }10\text{ and }15=30.
\displaystyle =\frac{27}{30}-\frac{14}{30}=\frac{13}{30}.

\displaystyle \text{(ii) }13-6\frac{2}{5}
\displaystyle =13-\frac{32}{5}
\displaystyle \text{L.C.M. of }1\text{ and }5=5.
\displaystyle =\frac{65}{5}-\frac{32}{5}=\frac{33}{5}=6\frac{3}{5}.

\displaystyle \text{(iii) }2\frac{13}{35}-1\frac{7}{30}
\displaystyle =\frac{83}{35}-\frac{37}{30}
\displaystyle \text{L.C.M. of }35\text{ and }30=210.
\displaystyle =\frac{498}{210}-\frac{259}{210}=\frac{239}{210}=1\frac{29}{210}.

\displaystyle \\

\displaystyle \textbf{Question 3: }\text{Evaluate:}
\displaystyle \text{(i) }3\frac{1}{4}-1\frac{5}{6}+2\frac{3}{8}\qquad\text{(ii) }2\frac{1}{18}-\frac{7}{12}-\frac{23}{24}
\displaystyle \text{(iii) }9\frac{5}{14}-6\frac{8}{21}+\frac{25}{42}
\displaystyle \text{Answer:}
\displaystyle \text{(i) }3\frac{1}{4}-1\frac{5}{6}+2\frac{3}{8}
\displaystyle =\frac{13}{4}-\frac{11}{6}+\frac{19}{8}
\displaystyle \text{L.C.M. of }4,\ 6,\ 8=24.
\displaystyle =\frac{78-44+57}{24}=\frac{91}{24}=3\frac{19}{24}.

\displaystyle \text{(ii) }2\frac{1}{18}-\frac{7}{12}-\frac{23}{24}
\displaystyle =\frac{37}{18}-\frac{7}{12}-\frac{23}{24}
\displaystyle \text{L.C.M. of }18,\ 12,\ 24=72.
\displaystyle =\frac{148-42-69}{72}=\frac{37}{72}.

\displaystyle \text{(iii) }9\frac{5}{14}-6\frac{8}{21}+\frac{25}{42}
\displaystyle =\frac{131}{14}-\frac{134}{21}+\frac{25}{42}
\displaystyle \text{L.C.M. of }14,\ 21,\ 42=42.
\displaystyle =\frac{393-268+25}{42}=\frac{150}{42}=\frac{25}{7}=3\frac{4}{7}.

\displaystyle \\

\displaystyle \textbf{Question 4: }\text{Evaluate:}
\displaystyle \text{(i) }\frac{9}{14}\times\frac{7}{3}\qquad\text{(ii) }6\frac{2}{3}\times3\frac{3}{4}\qquad\text{(iii) }3\frac{1}{3}\times\frac{18}{25}
\displaystyle \text{Answer:}
\displaystyle \text{(i) }\frac{9}{14}\times\frac{7}{3}=\frac{3\times3\times7}{2\times7\times3}=\frac{3}{2}=1\frac{1}{2}.

\displaystyle \text{(ii) }6\frac{2}{3}\times3\frac{3}{4}=\frac{20}{3}\times\frac{15}{4}
\displaystyle =\frac{4\times5\times3\times5}{3\times4}=25.

\displaystyle \text{(iii) }3\frac{1}{3}\times\frac{18}{25}=\frac{10}{3}\times\frac{18}{25}
\displaystyle =\frac{2\times5\times3\times6}{3\times5\times5}=\frac{12}{5}=2\frac{2}{5}.

\displaystyle \\

\displaystyle \textbf{Question 5: }\text{Evaluate:}
\displaystyle \text{(i) }18\div2\frac{2}{3}\qquad\text{(ii) }\frac{2}{3}\div3\frac{3}{4}\qquad\text{(iii) }4\frac{2}{3}\div7
\displaystyle \text{Answer:}
\displaystyle \text{(i) }18\div2\frac{2}{3}=\frac{18}{1}\div\frac{8}{3}
\displaystyle =\frac{18}{1}\times\frac{3}{8}=\frac{27}{4}=6\frac{3}{4}.

\displaystyle \text{(ii) }\frac{2}{3}\div3\frac{3}{4}=\frac{2}{3}\div\frac{15}{4}
\displaystyle =\frac{2}{3}\times\frac{4}{15}=\frac{8}{45}.

\displaystyle \text{(iii) }4\frac{2}{3}\div7=\frac{14}{3}\div\frac{7}{1}
\displaystyle =\frac{14}{3}\times\frac{1}{7}=\frac{2}{3}.

\displaystyle \\

\displaystyle \textbf{Question 6: }\text{Simplify:}
\displaystyle \text{(i) }1-2\frac{2}{5}\div4\frac{1}{2}\ \text{of}\ 2\frac{2}{3}\times\frac{5}{6}+\frac{1}{3}
\displaystyle \text{(ii) }1\div\frac{5}{7}\ \text{of}\ 6\frac{3}{10}-\frac{1}{6}
\displaystyle \text{(iii) }\left(\frac{1}{5}\div\frac{1}{5}\ \text{of}\ \frac{1}{5}\right)\div\left(\frac{1}{5}\ \text{of}\ \frac{1}{5}\div\frac{1}{5}\right)
\displaystyle \text{(iv) }5-\left[\frac{3}{4}+\left\{2\frac{1}{2}-\left(\frac{1}{2}+\frac{1}{6}-\frac{1}{7}\right)\right\}\right]
\displaystyle \text{(v) }\frac{1}{5}\left[5-\frac{1}{5}\left\{5-\frac{1}{5}\left(5-\frac{1}{5}\right)\right\}\right]\div1\frac{1}{5}
\displaystyle \text{(vi) }1+1\div\left\{1+1\div\left(1+\frac{1}{3}\right)\right\}
\displaystyle \text{(vii) }7\frac{1}{2}-\left[2\frac{1}{4}\div\left\{1\frac{1}{4}-\frac{1}{2}\left(1\frac{1}{2}-\frac{1}{3}-\frac{1}{6}\right)\right\}\right]
\displaystyle \text{(viii) }3\frac{1}{3}\div2\frac{1}{2}\times\frac{3}{4}\div\frac{1}{3}\ \text{of}\ 21\times1\frac{1}{6}
\displaystyle \text{(ix) }\frac{3}{4}\div2\frac{1}{4}\ \text{of}\ \frac{2}{3}-\left(\frac{1}{2}-\frac{1}{3}\right)\div\left(\frac{1}{2}+\frac{1}{3}\right)\times3\frac{1}{3}+\frac{5}{6}
\displaystyle \text{(x) }\left(3\frac{1}{4}-\frac{4}{5}\ \text{of}\ \frac{5}{6}\right)\div\left\{4\frac{1}{3}\div\frac{1}{5}-\left(\frac{3}{10}+21\frac{1}{5}\right)\right\}
\displaystyle \text{Answer:}
\displaystyle \text{(i) }1-2\frac{2}{5}\div4\frac{1}{2}\ \text{of}\ 2\frac{2}{3}\times\frac{5}{6}+\frac{1}{3}
\displaystyle =1-\frac{12}{5}\div\frac{9}{2}\ \text{of}\ \frac{8}{3}\times\frac{5}{6}+\frac{1}{3}
\displaystyle =1-\frac{12}{5}\div12\times\frac{5}{6}+\frac{1}{3}
\displaystyle =1-\frac{12}{5}\times\frac{1}{12}\times\frac{5}{6}+\frac{1}{3}
\displaystyle =1-\frac{1}{6}+\frac{1}{3}=\frac{7}{6}=1\frac{1}{6}.

\displaystyle \text{(ii) }1\div\frac{5}{7}\ \text{of}\ 6\frac{3}{10}-\frac{1}{6}
\displaystyle =1\div\frac{5}{7}\ \text{of}\ \frac{63}{10}-\frac{1}{6}
\displaystyle =1\div\frac{9}{2}-\frac{1}{6}
\displaystyle =\frac{2}{9}-\frac{1}{6}=\frac{4-3}{18}=\frac{1}{18}.

\displaystyle \text{(iii) }\left(\frac{1}{5}\div\frac{1}{5}\ \text{of}\ \frac{1}{5}\right)\div\left(\frac{1}{5}\ \text{of}\ \frac{1}{5}\div\frac{1}{5}\right)
\displaystyle =\left(\frac{1}{5}\div\frac{1}{25}\right)\div\left(\frac{1}{25}\div\frac{1}{5}\right)
\displaystyle =\left(\frac{1}{5}\times25\right)\div\left(\frac{1}{25}\times5\right)
\displaystyle =5\div\frac{1}{5}=5\times5=25.

\displaystyle \text{(iv) }5-\left[\frac{3}{4}+\left\{2\frac{1}{2}-\left(\frac{1}{2}+\frac{1}{6}-\frac{1}{7}\right)\right\}\right]
\displaystyle =5-\left[\frac{3}{4}+\left\{\frac{5}{2}-\left(\frac{1}{2}+\frac{1}{6}-\frac{1}{7}\right)\right\}\right]
\displaystyle =5-\left[\frac{3}{4}+\left\{\frac{5}{2}-\frac{11}{21}\right\}\right]
\displaystyle =5-\left[\frac{3}{4}+\frac{83}{42}\right]
\displaystyle =5-\frac{229}{84}=\frac{191}{84}=2\frac{23}{84}.

\displaystyle \text{(v) }\frac{1}{5}\left[5-\frac{1}{5}\left\{5-\frac{1}{5}\left(5-\frac{1}{5}\right)\right\}\right]\div1\frac{1}{5}
\displaystyle =\frac{1}{5}\left[5-\frac{1}{5}\left\{5-\frac{1}{5}\left(\frac{24}{5}\right)\right\}\right]\div\frac{6}{5}
\displaystyle =\frac{1}{5}\left[5-\frac{1}{5}\left\{5-\frac{24}{25}\right\}\right]\div\frac{6}{5}
\displaystyle =\frac{1}{5}\left[5-\frac{1}{5}\left(\frac{101}{25}\right)\right]\div\frac{6}{5}
\displaystyle =\frac{1}{5}\left[5-\frac{101}{125}\right]\div\frac{6}{5}
\displaystyle =\frac{1}{5}\times\frac{524}{125}\times\frac{5}{6}=\frac{262}{375}.

\displaystyle \text{(vi) }1+1\div\left\{1+1\div\left(1+\frac{1}{3}\right)\right\}
\displaystyle =1+1\div\left\{1+1\div\frac{4}{3}\right\}
\displaystyle =1+1\div\left(1+\frac{3}{4}\right)
\displaystyle =1+1\div\frac{7}{4}=1+\frac{4}{7}=\frac{11}{7}=1\frac{4}{7}.

\displaystyle \text{(vii) }7\frac{1}{2}-\left[2\frac{1}{4}\div\left\{1\frac{1}{4}-\frac{1}{2}\left(1\frac{1}{2}-\frac{1}{3}-\frac{1}{6}\right)\right\}\right]
\displaystyle =\frac{15}{2}-\left[\frac{9}{4}\div\left\{\frac{5}{4}-\frac{1}{2}\left(\frac{3}{2}-\frac{1}{3}-\frac{1}{6}\right)\right\}\right]
\displaystyle =\frac{15}{2}-\left[\frac{9}{4}\div\left\{\frac{5}{4}-\frac{1}{2}(1)\right\}\right]
\displaystyle =\frac{15}{2}-\left[\frac{9}{4}\div\frac{3}{4}\right]
\displaystyle =\frac{15}{2}-3=\frac{9}{2}=4\frac{1}{2}.

\displaystyle \text{(viii) }3\frac{1}{3}\div2\frac{1}{2}\times\frac{3}{4}\div\frac{1}{3}\ \text{of}\ 21\times1\frac{1}{6}
\displaystyle =\frac{10}{3}\div\frac{5}{2}\times\frac{3}{4}\div\frac{1}{3}\ \text{of}\ 21\times\frac{7}{6}
\displaystyle =\frac{10}{3}\div\frac{5}{2}\times\frac{3}{4}\div7\times\frac{7}{6}
\displaystyle =\frac{10}{3}\times\frac{2}{5}\times\frac{3}{4}\times\frac{1}{7}\times\frac{7}{6}=\frac{1}{6}.

\displaystyle \text{(ix) }\frac{3}{4}\div2\frac{1}{4}\ \text{of}\ \frac{2}{3}-\left(\frac{1}{2}-\frac{1}{3}\right)\div\left(\frac{1}{2}+\frac{1}{3}\right)\times3\frac{1}{3}+\frac{5}{6}
\displaystyle =\frac{3}{4}\div\frac{9}{4}\ \text{of}\ \frac{2}{3}-\frac{1}{6}\div\frac{5}{6}\times\frac{10}{3}+\frac{5}{6}
\displaystyle =\frac{3}{4}\div\frac{3}{2}-\frac{1}{6}\times\frac{6}{5}\times\frac{10}{3}+\frac{5}{6}
\displaystyle =\frac{3}{4}\times\frac{2}{3}-\frac{2}{3}+\frac{5}{6}
\displaystyle =\frac{1}{2}-\frac{2}{3}+\frac{5}{6}=\frac{2}{3}.

\displaystyle \text{(x) }\left(3\frac{1}{4}-\frac{4}{5}\ \text{of}\ \frac{5}{6}\right)\div\left\{4\frac{1}{3}\div\frac{1}{5}-\left(\frac{3}{10}+21\frac{1}{5}\right)\right\}
\displaystyle =\left(\frac{13}{4}-\frac{4}{5}\times\frac{5}{6}\right)\div\left\{\frac{13}{3}\times5-\left(\frac{3}{10}+\frac{106}{5}\right)\right\}
\displaystyle =\left(\frac{13}{4}-\frac{2}{3}\right)\div\left\{\frac{65}{3}-\frac{43}{2}\right\}
\displaystyle =\frac{31}{12}\div\frac{1}{6}
\displaystyle =\frac{31}{12}\times6=\frac{31}{2}=15\frac{1}{2}.

\displaystyle \\

Discover more from ICSE / ISC / CBSE Mathematics Portal for K12 Students

Subscribe to get the latest posts sent to your email.