SChand Composite Mathematics Class 7 Chapter 2 Fractions Exercise 2A

Exercise 2A

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Q1 | Ex-2A |Class 8 | Fractions | S.Chand | Composite Mathematics | Chapter 2 | myhelper

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Question 1

Add or Subtract write each answer in Simplest form

(i) $\frac{7}{9}+\frac{1}{8}$

Sol :

L.C.M of 9 and 8 is 72

$=\frac{7 \times 8+1 \times 9}{72}$

$=\frac{56+9}{72}=\frac{65}{72}$

(ii) $\frac{5}{8}-\frac{1}{2}$

Sol :

L.C.M of 8 and 2 is 8

$\frac{5 \times 1- 1 \times 4}{8}=\frac{5-4}{8}=\frac{1}{8}$

(iii) $3 \frac{1}{8}+1 \frac{5}{6}$

Sol :

$= \frac{3 \times 8+1}{8}+ \frac{1 \times 6 +5}{6}$

L.C.M of 8 and 6 is 24

$=\frac{25}{8}+\frac{11}{6}$

$=\frac{25\times 3+11 \times 4}{24}=\frac{75+44}{24}$

$=\frac{119}{24}=4\frac{23}{24}$

(iv) $16 \frac{5}{7}-8 \frac{2}{5}$

Sol :

$=\frac{16 \times 7+5}{7}-\frac{8 \times 5+2}{5}$

$=\frac{117}{7}-\frac{42}{5}$

L.C.M of 7 and 5 is 35

$=\frac{117 \times 5- 42 \times 7}{35}=\frac{585-294}{35}$

$=\frac{291}{35}=8\frac{11}{35}$

(v) $13 \frac{1}{5}+2 \frac{1}{2}+\frac{3}{5}$

Sol :

$=\frac{13 \times 5+1}{5}+\frac{2 \times 2+1}{2}+\frac{3}{5}$

$=\frac{66}{5}+\frac{5}{2}+\frac{3}{5}$

L.C.M of 5 and 2 is 10

$=\frac{66 \times 2 + 5 \times 5+3 \times 2}{10}$

$=\frac{132 + 25 + 6}{10}=\frac{163}{10}=16\frac{3}{10}$

(vi) $36 \frac{7}{9}-\left(12 \frac{4}{5}+11 \frac{1}{3}\right)$

Sol :

$=\frac{36 \times 9 +7}{9}-\frac{12 \times 5+4}{5}+\frac{11 \times 3+1}{3}$

$=\frac{331}{9}-\left(\frac{64}{5}+\frac{34}{3}\right)$

L.C.M of 9 , 5 , 3 is 45

$=\frac{331}{9}-\frac{64}{5}-\frac{34}{3}$

$=\frac{331 \times 5-64 \times 9-34 \times 15}{45}$

$=\frac{1655-576-510}{45}=\frac{165-1086}{45}$

$=\frac{569}{45}=12\frac{29}{45}$

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Q2 | Ex-2A |Class 8 | Fractions |S.Chand | Composite Mathematics | Chapter 2 | myhelper

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Question 2

Simplify :

(i) $\frac{3}{7}+\frac{1}{21}-\frac{1}{14}$

Sol :

L.C.M of  7 , 21, 14 is 42

$=\frac{3 \times 6+1 \times 2-1 \times 3}{42}$

$=\frac{18+2-3}{42}=\frac{17}{42}$

(ii) $\frac{1}{2}-\frac{1}{4}+\frac{5}{8}$

Sol :

L.C.M of  2 , 4 , 8 is 8

$=\frac{1 \times 4-1 \times 2+5 \times 1}{8}$

$=\frac{4-2+5}{8}=\frac{7}{8}$

(iii) $18 \frac{2}{3}-15 \frac{5}{6}+4 \frac{1}{8}$

Sol :

L.C.M of 3,  6 , 8 is 24

$=\frac{18 \times 3 +2}{3}-\frac{15 \times 6+5}{6}+\frac{4\times 8+1}{8}$

$\frac{56}{3}-\frac{95}{6}+\frac{33}{8}$

$=\frac{56 \times 8-95 \times 4+ 33 \times 3}{24}=\frac{448-380+99}{24}$

$=\frac{167}{24}=6\frac{23}{24}$

(iv) $22 \frac{9}{11}-8 \frac{1}{4}-2 \frac{1}{6}$

Sol :

L.C.M of  11 , 4 , 6 is 132

$=\frac{22 \times 11 +9}{11}-\frac{8 \times 4+1}{4}-\frac{2 \times 6+1}{6}$

$=\frac{251}{11}-\frac{33}{4}-\frac{13}{6}$

$=\frac{251 \times 12-33 \times 33-13 \times 22}{132}$

$=\frac{3012-1089-286}{132}=\frac{3012-1375}{132}$

$=\frac{1637}{132}=12\frac{53}{132}$

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Q3 | Ex-2A |Class 8 | Fractions |S.Chand | Composite Mathematics | Chapter 2 | myhelper

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Question 3

Compare using < or > :

(i) $\frac{1}{4}+\frac{1}{7} \square \frac{1}{12}+\frac{5}{6}$

Sol :

LCM of 4 , 7 is 28 and 12 , 6 is 12

 $=\frac{1 \times 7+1 \times 4}{28} \square \frac{1 \times 1+5 \times 2}{12}$

 $=\frac{7+4}{28} \square \frac{1+10}{12}$

 $=\frac{11}{28} \square \frac{11}{12}$

On Cross multiplying

11×12<11×28

 ∴$\frac{1}{4}+\frac{1}{7}< \frac{1}{12}+\frac{5}{6}$

(ii) $\frac{5}{8}-\frac{1}{6} \square \frac{8}{9}-\frac{2}{3}$

Sol :

L.C.M of  8 , 6 is 24 and 9 ,3 is 9

$=\frac{5\times 3-1 \times 4}{24} \square \frac{8 \times 1-2 \times 3}{9}$

$=\frac{15-4}{24} \square \frac{8-6}{9}$

$=\frac{11}{24} \square \frac{2}{9}$

On Cross multiplying

11×9 > 2×24

∴$\frac{5}{8}-\frac{1}{6} >  \frac{8}{9}-\frac{2}{3}$

(iii) $6 \frac{2}{3}-2 \frac{1}{3} \square 4$

Sol :

$\frac{6\times 3+2}{3}- \frac{2 \times 3+1}{3} \square 4$

$\frac{20}{3}- \frac{7}{3} \square 4$

$\frac{20-7}{3} \square 4$

$\frac{13}{3} \square 4$

On Cross multiplying

13×1>3×4

∴$6 \frac{2}{3}-2 \frac{1}{3} > 4$

(iv) $7 \frac{1}{12}+3 \frac{1}{3} \square 11$

Sol :

$\frac{7\times 12+1}{12}+\frac{3 \times 3+1}{3} \square 11$

$\frac{85}{12}+\frac{10}{3} \square 11$

L.C.M of 12 and 3 is 12

$\frac{85 \times 1+10 \times 4}{12} \square 11$

$\frac{85+40}{12} \square 11$

$\frac{125}{12} \square 11$

On Cross multiplying

125×1<11×12

$7 \frac{1}{12}+3 \frac{1}{3} < 11$