EXERCISE 2.1
Question 1
(i) Total 8 parts , 2 were shaded
$\therefore \frac{2}{8} \mathrm{th}$ part is shaded i.e $\frac{2}{8}=\frac{1}{4}$
(ii) Total 10 parts , 3 were shaded
$\therefore \frac{3}{10}$th part is shaded
(iii) Total 12 Parts , 5 were shaded.
$\therefore \frac{5}{12}$ th part is shaded.
(iv) Total 13 parts , 7 were shaded
$\therefore \frac{7}{13}$ th part is shaded.
Question 2
Let the fraction be x
$x \times 60=35$
$x=\frac{35}{60}$
$x=\frac{7}{12}$ th fraction.
Question 3
i) $2 \frac{7}{9}=2+\frac{7}{9}=\frac{2 \times 9+7}{9}=\frac{25}{9}$
ii) $5 \frac{4}{11}=5+\frac{4}{11}=\frac{5 \times 11+4}{11}=\frac{59}{11}$
Question 4
i) $\frac{73}{8}=\frac{9 \times 8+1}{8}=9+\frac{1}{8}=9 \frac{1}{8}$
ii) $\frac{94}{13}=\frac{13 \times 7+3}{13}=7+\frac{3}{13}=7 \frac{3}{13}$
Question 5
$\begin{aligned} \text { i) } \frac{3}{7}=\frac{x}{35} & \\ 3 \times 35=& 2 \times x \\ x &=\frac{3 \times 35}{{x}} \\ & x=15 \text { is missing namber } \end{aligned}$
(ii)
$\begin{aligned} \frac{5}{x}=\frac{30}{18} & \\ 5 \times 18 &=30 \times x \\ & x=\frac{5 \times 18}{30} \end{aligned}$
(iii) $\frac{x}{9}=\frac{56}{32}$
$x \times 72=9 \times 56$
$x=\frac{9 \times 56}{72}$
$x=7$ is Missing number
Question 6
(i) $\frac{48}{72}$
HCF of 48 and 72 is 24
Divide the numerator and denominator of given fraction by 24
$\frac{48}{72}=\frac{48 \div 24}{72 \div 24}=\frac{2}{3} .$
(ii) $\frac{276}{115}$
HCF of 276 , 115 is 23.
(iii) $\frac{72}{336}$
HCF of 72,336 is 24
Divide numerator and denominator by 24
$\frac{72}{336}=\frac{72 \div 29}{336 \div 24}=\frac{3}{14}$
Question 7
(i) $\mathrm{LCM}$ of $4,6,8$ is 24
$\frac{3}{4}=\frac{3 \times 6}{4 \times 6}=\frac{18}{24}$
$\frac{5}{6}=\frac{5 \times 4}{6 \times 4}=\frac{20}{24}$
$\frac{7}{8}=\frac{7 \times 3}{8 \times 3}=\frac{21}{24}$
Thus the given fractions are equivalent to $\frac{18}{24}, \frac{20}{24}, \frac{21}{24}$
(ii) $\mathrm{LCM}$ of $25,10,40$ is 200 .
$\frac{7}{25}=\frac{7 \times 8}{25 \times 8}=\frac{56}{200}$
$\frac{9}{10}=\frac{9 \times 20}{10 \times 20}=\frac{180}{200}$
$\frac{19}{40}=\frac{19 \times 5}{40 \times 5}=\frac{95}{200}$
Thus the given fractions are equivalent to $\frac{56}{200}, \frac{180}{200}, \frac{95}{200}$
Question 8
(i) LCM of 9,3,21 is 63
$\frac{2}{9}=\frac{2 \times 3}{9 \times 7}=\frac{14}{63}$
$\frac{2}{3}=\frac{2 \times 21}{3 \times 21}=\frac{42}{63}$
$\frac{8}{21}=\frac{8 \times 3}{21 \times 3}=\frac{24}{63}$
Descending order is $\frac{2}{3}, \frac{8}{21}, \frac{2}{9}$
(ii) LCM of 5,7,10=70
$\frac{1}{5}=\frac{1 \times 14}{5 \times 14}=\frac{14}{70}$
$\frac{3}{7}=\frac{3 \times 10^{-}}{7 \times 10}=\frac{30}{70}$
$\frac{7}{10}=\frac{7 \times 7}{10 \times 7}=\frac{49}{70}$
Descending order is $\frac{7}{10}, \frac{3}{7}, \frac{1}{5}$
Question 9
(i) LCM of 7,8,14,21 is 168
$\frac{5}{7}=\frac{5 \times 24}{7 \times 24}=\frac{120}{168}$
$\frac{3}{8}=\frac{3 \times 21}{8 \times 21}=\frac{63}{168}$
$\frac{9}{14}=\frac{9 \times 12}{14 \times 12}=\frac{108}{168}$
$\frac{20}{21}, \frac{20 \times 8}{21 \times 8}=\frac{160}{168}$
Ascending order is $\frac{3}{8}, \frac{9}{14}, \frac{5}{7}, \frac{20}{21}$
(ii) LCM of $18,15,24,12$ is 360
$\frac{13}{18}=\frac{13 \times 20}{18 \times 20}=\frac{260}{360}$
$\frac{8}{15}=\frac{8 \times 24}{15 \times 24}=\frac{192}{360}$
$\frac{17}{24}=\frac{17 \times 15}{24 \times 15}=\frac{255}{360}$
$\frac{7}{12}=\frac{7 \times 30}{12 \times 30}=\frac{210}{360}$
Ascending order is $\frac{8}{15}, \frac{7}{12}, \frac{12}{24}, \frac{13}{18}$
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