Given:$(i)$. $\frac{7}{24\ }- \frac{17}{36}$$(ii)$. $\frac{5}{63}-\ (-\frac{6}{21})$$(iii)$. $-\frac{6}{13}\ -\ (-\frac{7}{15})$$(iv)$. $-\frac{3}{8}-\frac{7}{11}$$(v)$. $-2\frac{1}{9}\ -\ 6$To do: To solve the given expression.Solution:  $(i)$. $\frac{7}{24\ }- \frac{17}{36}$$=\frac{7\times 3}{24\times 3}-\frac{17\times 2}{36\times 2}$       [LCM of $24$ and $36$ is $72$ ]$=\frac{21-34}{72}$$=-\frac{13}{72}$$(ii)$. $\frac{5}{63}-\ (-\frac{6}{21})$$=\frac{5\times 1}{63\times 1}-(-\frac{6\times 3}{21\times 3})$    [LCM of 63 and 21 is 63]$=\frac{5-\left(-18\right)}{63}$$=\frac{23}{63}$$(iii)$. ... Read More

Given: $(i)$. $\frac{5}{4}+(-\frac{11}{4})$$(ii)$. $\frac{5}{3}+\frac{3}{5}$$(iii)$. $\frac{-9}{10}+\ \frac{22}{15}$$(iv)$. $\frac{-3}{-11}+\frac{5}{9}$$(v)$. $\frac{-8}{19}+(-\frac{2}{57})$ $(vi)$. $-\frac{2}{3}+0$$(vii)$. $-2\frac{1}{3}\ +\ 4\frac{3}{5}$To do: To find the sum of the given expressions. Solution: $(i)$. $\frac{5}{4}+(-\frac{11}{4})$$=\frac{5}{4}-\frac{11}{4}$$=\frac{5-11}{4}$$=\frac{-6}{4}$$(ii)$. $\frac{5}{3}+\frac{3}{5}$$=\frac{5\times 5}{3\times 5}+\frac{3\times 3}{5\times 3}$                [On taking LCM of 3 and 5, we obtain 15]$=\frac{25}{15}+\frac{9}{15}$$=\frac{25+9}{15}$$=\frac{34}{15}$$(iii)$. $\frac{-9}{10}+\ \frac{22}{15}$$=\frac{-9\times 3}{10\times 3}+\frac{22\times 2}{15\times 2}$    ... Read More

Given: In an isosceles right-angled triangle $ABC$, where $m\angle ACB = 90^{\circ}$ and $AC = 6\ cm$.To do: To construct $\triangle ABC$.Steps of construction:At first, let us draw a line segment $AC=6\ cm$.At $C$, draw a perpendicular such that $CX\perp AC$.Let us assume $C$ as a center and draw an arc ... Read More

Given: The points P, Q, R, S, T, U, A and B on the number line are such that, $TR = RS = SU$ and $AP = PQ = QB$.To do: To name the rational numbers represented by P, Q, R, and S.Solution:Numbers represented by R and S:Points U, S, R, ... Read More

To do: To find:(a) $15 \%$ of $250$(b).$1 \%$ of $1$ hour(c) $20 \%$ of $Rs.\ 2500$(d) $75 \%$ of $1\ kg$Solution:$(a).\ 15$ % of $250$$=\frac{15}{100}\times250$$=15\times2.5=37.5$$(b).\ 1$ % of $1\ hours$$=1$ % of $60\ minutes$$=1$ % of $(60\times 60)\ seconds$$=\frac{1}{100}\times60\times60$$=6\times6=36$$(c).\ 20$ % of $Rs.\ 2500$$=\frac{20}{100}\times2500$$=20\times25$$=Rs.\ 500$$(d).\ 75$ % of $1\ kg$$=75$ % of $1000\ g$$=\frac{75}{100}\times1000$$=750g=0.750\ kg$

To do: To fiind the whole quantity if:$(a).\ 5$ % of it is $600$. $(b).\ 12$ % of it is $Rs.\ 1080$.$(c).\ 40$ % of it is $500\ km$.$(d).\ 70$ % of it is $14$ minutes. $(e).\ 8$ % of it is $40\ litres$.Solution:$(a)$. Let us assume the whole quantity be $x$, ... Read More

Given: $(a).\ 25$ %  $(b).\ 150$ %  $(c).\ 20$ % $(d).\ 5$ %To do: To convert given per cents to decimal fractions and also to fractions in simplest forms.Solution:$(a).\ 25$ %The decimal fraction will be, $=\frac{25}{100}$$=0.25$The simplest form of the fraction will be$\frac{25}{100}=\frac{5}{100}$$=\frac{1}{4}$$(b).\ 150$ %The decimal fraction will be, $=\frac{150}{100}$$=1.5$The simplest ... Read More

Given: In a city $30$ % are females and $40$ % are males and the remaining are children.To find: We have to find the percentage of children in the city.Solution: Total percent $=100$ %Females$=30$ %Males$=40$ %So,Children$=100$ %$-(30$ % $+40$ %$)$Children$=100$ %$-70$ %Children$=30$ %

Given: Out of $15, 000$ voters in a constituency, $60 \%$ voted.To do: To find the percentage of voters who did not vote. And to find how many actually did not vote.Solution:Total voters $= 15, 000$Percentage of voted candidates $=60$ %Percentage of not voted candidates $=100-60=40$ %Actual candidates, who did not vote ... Read More

Given: Meeta saves $Rs.\ 4000$ from her salary. This is $10 \%$ of her salary. To do: To find her salary.Solution: Let Meera’s salary be Rs. $x$.Now, 10% of salary $= Rs.\ 400$$\Rightarrow\ 10$ % of $x = Rs.\ 400$$\Rightarrow\ \frac{10}{100}\times x=400$$\Rightarrow x=\frac{400\times100}{10}$$\Rightarrow\ x=4000$Hence, Meera’s salary is $Rs.\ 4, 000$Read More