EXERCISE 2.2
Question 1
(i) $\frac{4}{3}+\frac{3}{8}$
$\mathrm{LCM}$ of 3,8 is 24
$=\frac{4 \times 8+7 \times 3}{24}$
$=\frac{32+21}{24}=\frac{53}{24}$
(ii) $8 \frac{1}{2}-3 \frac{5}{8}$
$8 \frac{1}{2}=8+\frac{1}{2}=\frac{8 x 2+1}{2}=\frac{16+1}{2}=\frac{17}{2}$
$3 \frac{5}{8}=3+\frac{5}{8 .}=\frac{3 \times 8+5}{8}=\frac{24+5}{8}=\frac{29}{8}$
$=\frac{17}{2}-\frac{29}{8}$
$=\frac{17 \times 4-29 \times 1}{8}$
$=\frac{68-29}{8}$
$=\frac{39}{8}$
(iii) $\frac{5}{12}+\frac{1}{18}-\frac{2}{9}$
Lcm of $12,18,9$ is 36
$=\frac{5 \times 3+1 \times 2-2 \times 4}{36}$
$=\frac{15+2-8}{36}$
$=\frac{9}{36}$
$=\frac{1}{4}$
Question 2
(i) $7 \frac{3}{4}=7+\frac{3}{4}=\frac{7 \times 4+3}{4}=\frac{28+3}{4}=\frac{31}{4}$
$3 \frac{5}{6}=3+\frac{5}{6}=\frac{3 \times 6+5}{6}=\frac{18+5}{6}=\frac{23}{6}$
$=\frac{31}{4}-\frac{23}{6}+\frac{7}{8}$
$\begin{array}{r|l}2&4,6,8\\ \hline 2& 2,3,4 \\ \hline&1,3,2\end{array}$
LCM =24
$=\frac{31 \times 6-23 \times 4+7 \times 3}{24}$
$=\frac{186-92+21}{24}$
$=\begin{array}{l}\frac{207-92}{24} \\ =\frac{115}{24} .\end{array}$
(ii)$6 \frac{1}{8}=6+\frac{1}{8}=\frac{6 \times 8+1}{8}=\frac{49}{8}$
$2 \frac{1}{12}=2+\frac{1}{12} = \frac{2 \times 12+1}{12}=\frac{25}{12}$
$5 \frac{1}{10}=5+\frac{1}{10}=\frac{5 \times 10+1}{10}=\frac{51}{10}$
$3 \frac{7}{25}=3+\frac{7}{25}=\frac{3 \times 25+7}{25}=\frac{75+7}{25}=\frac{82}{25}$
$=\frac{49}{8}-\frac{25}{12}-\frac{51}{10}+\frac{82}{25}$
$\begin{array}{r|l}2&8,10,12,25\\ \hline 5& 4,5,6,25 \\ \hline 2&4,1,6,5\\ \hline&2,1,3,5\end{array}$
LCM = 600
$=\frac{49 \times 75-25 \times 50-51 \times 60+82 \times 24}{600}$
$=\frac{1333}{600}$
Question 3
Jaishree studies daily for $5 \frac{2}{3}$ hours
i.e $5+\frac{2}{3}=\frac{5 \times 3+2}{3}=\frac{17}{3}$ hours
She devoted has time for science and mathematics $2 \frac{4}{5}=2+\frac{4}{5}=\frac{2 \times 5+4}{5}=\frac{14}{5}$ hours
Total time = $\frac{17}{3}$ hrs
Let the time for other subject be x
$\begin{aligned} \frac{14}{5}+x &=\frac{17}{3} \\ x &=\frac{17}{3}-\frac{14}{5} \\ x &=\frac{17 \times 5-14 \times 3}{15} \end{aligned}$
$x=\frac{85-42}{15}$
$x=\frac{43}{15}$ hrs for other subjects
Question 4
Ramesh solved $\frac{2}{7}$ part of an exercise
Reshma solved $\frac{4}{5}$ part
LCM of 7, 5 is 35
$\frac{2}{7}=\frac{2 \times 5}{7 \times 5}=\frac{10}{35} ; \frac{4}{5}=\frac{4 \times 7}{5 \times 3}=\frac{28}{35}$
$\frac{4}{5}>\frac{2}{7}$
i.e Ramesh Solved lesser part and by $\frac{28}{35}-\frac{10}{35}$ i.e $\frac{18}{35}$ part
Question 5
Sohali had Rs $35 \frac{3}{5}$ i.e $\frac{35 \times 5+3}{5}$ = Rs $\frac{178}{5}$
She got Rs $16 \frac{1}{15}$ From her mother
i.e $\frac{16 \times 15+1}{15}=₹ \frac{241}{15}$
She spent on food Rs $28 \frac{2}{3}=\frac{28 \times 3+2}{3}$
=Rs $\frac{86}{3}$
Money left = ?
Total money she had = Rs $\frac{178}{5}+\frac{241}{15}$
$=\frac{178 \times 3+241 \times 1}{15}$
$=\frac{534+241}{15}$
$=\frac{275}{15}$
Out of which she spent Rs on food i.e $\frac{86}{3}$
ஃ Money left = Rs $\frac{775}{15}-\frac{86}{3}$
=$\frac{775 \times 1-8 \times 5}{15}$
=$\frac{77-430}{15}$
=$\frac{345}{15}$
=$₹ 23$
ஃ She had left with Rs 23 with her
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