To do :We have to solve the given expressions. Solution :(a) $\frac{2}{3} + \frac{1}{7}$LCM of denominators 3 and 7 is 21.This implies, $\frac{2}{3} + \frac{1}{7}=\frac{2\times7+1\times3}{21}$$= \frac{14+3}{21}$$=\frac{17}{21}$The value of $\frac{2}{3} + \frac{1}{7}$ is $\frac{17}{21}$.(b) $\frac{3}{10} + \frac{7}{15}$LCM of denominators 10 and 15 is 30.This implies, $\frac{3}{10} + \frac{7}{15}=\frac{3\times3+7\times2}{30}$$= \frac{9+14}{30}$$=\frac{23}{30}$The value of $\frac{3}{10} ... Read More

 Given:Sarita bought \( \frac{2}{5} \) metre of ribbon and Lalita \( \frac{3}{4} \) metre of ribbon. To do :We have to find the total length of the ribbon they boughtSolution :Length of the ribbon bought by Sarita $= \frac{2}{5}\ m$Length of the ribbon bought by Lalita $= \frac{3}{4}\ m$Therefore, Total length ... Read More

Given:Portion of cake given to Naina $=1\frac{1}{2}$Portion of cake given to Najma $=1\frac{1}{3}$To do: We have to find the total portion of cake given to Naina and Najma.Solution: The total portion of the cake given to Naina and Nagma $=$Portion of cake given to Naina $+$ Portion of cake given to Najma$=1\frac{1}{2} \ ... Read More

To do: We have to fill in the boxes.Solution: (a) Let the number in the box be $x$.This implies, $x-\frac{5}{8}=\frac{1}{4}$$x=\frac{1}{4}+\frac{5}{8}$$x=\frac{1\times2+5\times1}{8}$$x=\frac{2+5}{8}$$x=\frac{7}{8}$The number in the box is $\frac{7}{8}$.(b) Let the number in the box be $x$.This implies, $x-\frac{1}{5}=\frac{1}{2}$$x=\frac{1}{2}+\frac{1}{5}$$x=\frac{1\times5+1\times2}{10}$$x=\frac{5+2}{10}$$x=\frac{7}{10}$The number in the box is $\frac{7}{10}$.(c) Let the number in the box be $x$.This implies, $\frac{1}{2}-x=\frac{1}{6}$$x=\frac{1}{2}-\frac{1}{6}$$x=\frac{1\times3-1\times1}{6}$$x=\frac{3-1}{6}$$x=\frac{2}{6}$$x=\frac{1}{3}$The ... Read More

To do:  We have to complete the addition-subtraction boxes.Solution: (a) $\frac{2}{3}+\frac{4}{3}=\frac{2+4}{3}$$=\frac{6}{3}$$=2$$\frac{1}{3}+\frac{2}{3}=\frac{1+2}{3}$$=\frac{3}{3}$$=1$ $\frac{2}{3}-\frac{1}{3}=\frac{2-1}{3}$$=\frac{1}{3}$$\frac{4}{3}-\frac{2}{3}=\frac{4-2}{3}$$=\frac{2}{3}$$2-1=1$(b) $\frac{1}{2}+\frac{1}{3}=\frac{1\times3+1\times2}{6}$$=\frac{5}{6}$$\frac{1}{3}+\frac{1}{4}=\frac{1\times4+1\times3}{12}$$=\frac{4+3}{12}$$=\frac{7}{12}$ $\frac{1}{2}-\frac{1}{3}=\frac{1\times3-1\times2}{6}$$=\frac{3-2}{6}$$=\frac{1}{6}$$\frac{1}{3}-\frac{1}{4}=\frac{1\times4-1\times3}{12}$$=\frac{4-3}{12}$$=\frac{1}{12}$$\frac{5}{6}-\frac{7}{12}=\frac{5\times2-7\times1}{12}$$=\frac{10-7}{12}$$=\frac{3}{12}$$=\frac{1}{4}$ Read More

To do:We have to write '$ \) ', '$=$' between the given pairs of fractions.Solution:(a) \( \frac{1}{2} \square \frac{1}{5} \)Here, the numerators are same.Therefore, the fraction having lesser denominator will be lesser.This implies, $\frac{1}{2} > \frac{1}{5}$(b) $\frac{2}{4}=\frac{1\times2}{2\times2}$$=\frac{1}{2}$$\frac{3}{6}=\frac{1\times3}{2\times3}$$=\frac{1}{2}$This implies, $\frac{2}{4} = \frac{3}{6}$(c) LCM of denominators 5 and 3 is 15.This implies, ... Read More

To do:We have to change the given fractions to their simplest form.Solution:(a) $\frac{2}{12}=\frac{2\times1}{2\times6}$$=\frac{1}{6}$Therefore, The simplest form of \( \frac{2}{12} \) is $\frac{1}{6}$.(b) $\frac{3}{15}=\frac{3\times1}{3\times5}$$=\frac{1}{5}$Therefore, The simplest form of \( \frac{3}{15} \) is $\frac{1}{5}$.(c) $\frac{8}{50}=\frac{2\times4}{2\times25}$$=\frac{4}{25}$Therefore, The simplest form of \( \frac{8}{50} \) is $\frac{4}{25}$.(d) $\frac{16}{100}=\frac{4\times4}{4\times25}$$=\frac{4}{25}$Therefore, The simplest form of \( \frac{16}{100} \) ... Read More

To do:We have to find whether the given statements are true.Solution:(a) To check whether \( \frac{5}{9} \) is equal to \( \frac{4}{5} \), we have to convert them to like fractions.LCM of denominators 9 and 5 is 45.This implies, $\frac{5}{9}\times\frac{5}{5}=\frac{25}{45}$$\frac{4}{5}\times\frac{9}{9}=\frac{36}{45}$ $25 ≠ 36$This implies, $\frac{36}{45} ≠ \frac{25}{45}$Therefore, \( \frac{5}{9} \) ... Read More

Given:Ila read 25 pages of a book containing 100 pages. Lalita read \( \frac{2}{5} \) of the same book. To do:We have to find who among the two read less.Solution:Total number of pages in the book $= 100$ pagesNumber of pages read by Ila $=25$ pagesNumber of pages read by Lalita ... Read More

Given:Rafiq exercised for \( \frac{3}{6} \) of an hour, while Rohit exercised for \( \frac{3}{4} \) of an hour.To do:We have to find who exercised for a longer time.Solution:Time exercised by Rafiq $= \frac{3}{6}$ of an hour$=\frac{3}{6}\times60$ minutes$=3\times10$ minutes$=30$ minutesTime exercised by Rohit $= \frac{3}{4}$ of an hour$=\frac{3}{4}\times60$ minutes$=3\times15$ minutes$=45$ ... Read More