Fractions and Decimals - Solutions

 CBSE Class –VII Mathematics

NCERT Solutions
Chapter 2 Fractions and Decimals (Ex. 2.1)

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Question 1. Solve:

(i)2-35$\frac{3}{5}$          (ii) 4 + 78$\frac{7}{8}$       (iii)35+27$\frac{3}{5}+\frac{2}{7}$    (iv) 911−415$\frac{9}{11}-\frac{4}{15}$

(v)710+25+32$\frac{7}{10}+\frac{2}{5}+\frac{3}{2}$    (vi)i223+312$2\frac{2}{3}+3\frac{1}{2}$ 

(vii)812−358$8\frac{1}{2}-3\frac{5}{8}$

Answer: (i) 2−35$2-\frac{3}{5}$ = 10−35=75$\frac{10-3}{5}=\frac{7}{5}$ = 125$1\frac{2}{5}$

(ii)4+78$4+\frac{7}{8}$ = 32+78=398$\frac{32+7}{8}=\frac{39}{8}$ = 478$4\frac{7}{8}$

(iii)35+27$\frac{3}{5}+\frac{2}{7}$ = 21+1035$\frac{21+10}{35}$ = 3135$\frac{31}{35}$

(iv)911−415$\frac{9}{11}-\frac{4}{15}$ = 135−44165=91165$\frac{135-44}{165}=\frac{91}{165}$

(v) 710+25+32$\frac{7}{10}+\frac{2}{5}+\frac{3}{2}$ = 7+4+1510$\frac{7+4+15}{10}$ = 2610=135$\frac{26}{10}=\frac{13}{5}$ = 235$2\frac{3}{5}$

(vi) 223+312$2\frac{2}{3}+3\frac{1}{2}$ = 83+72$\frac{8}{3}+\frac{7}{2}$ = 16+216$\frac{16+21}{6}$ = 376$\frac{37}{6}$ = 616$6\frac{1}{6}$

(vii)812−358$8\frac{1}{2}-3\frac{5}{8}$ = 172−298$\frac{17}{2}-\frac{29}{8}$ = 68−298$\frac{68-29}{8}$ = 398$\frac{39}{8}$ = 478$4\frac{7}{8}$

Question 2. Arrange the following in descending order:

(i) 29,23,821$\frac{2}{9},\frac{2}{3},\frac{8}{21}$

(ii) 15,37,710$\frac{1}{5},\frac{3}{7},\frac{7}{10}$

Answer: (i) 29,23,821$\frac{2}{9},\frac{2}{3},\frac{8}{21}$ ⇒$\Rightarrow$ 1463,4263,2463$\frac{14}{63},\frac{42}{63},\frac{24}{63}$ [Converting into like fractions]

⇒$\Rightarrow$ 4263>2463>1463$\frac{42}{63}>\frac{24}{63}>\frac{14}{63}$ [Arranging in descending order]

Therefore, 23>821>29$\frac{2}{3}>\frac{8}{21}>\frac{2}{9}$

(ii) 15,37,710$\frac{1}{5},\frac{3}{7},\frac{7}{10}$ ⇒$\Rightarrow$1470,3070,4970$\frac{14}{70},\frac{30}{70},\frac{49}{70}$ [Converting into like fractions]

⇒$\Rightarrow$ 4970>3070>1470$\frac{49}{70}>\frac{30}{70}>\frac{14}{70}$ [Arranging in descending order]

Therefore, 710>37>15$\frac{7}{10}>\frac{3}{7}>\frac{1}{5}$

Question 3. In a “magic square”, the sum of the numbers in each row, in each column and along the diagonals is the same. Is this a magic square?

411$\frac{4}{11}$	911$\frac{9}{11}$	211$\frac{2}{11}$
311$\frac{3}{11}$	511$\frac{5}{11}$	711$\frac{7}{11}$
811$\frac{8}{11}$	111$\frac{1}{11}$	611$\frac{6}{11}$

(Along the first row 411+911+211=1511)$\left(\text{Along the first row }\frac{4}{11}+\frac{9}{11}+\frac{2}{11}=\frac{15}{11}\right)$

Answer: Sum of first row = 411+911+211=1511$\frac{4}{11}+\frac{9}{11}+\frac{2}{11}=\frac{15}{11}$ [Given]

Sum of second row = 311+511+711=3+5+711=1511$\frac{3}{11}+\frac{5}{11}+\frac{7}{11}=\frac{3+5+7}{11}=\frac{15}{11}$

Sum of third row = 811+111+611=8+1+611=1511$\frac{8}{11}+\frac{1}{11}+\frac{6}{11}=\frac{8+1+6}{11}=\frac{15}{11}$

Sum of first column = 411+311+811=4+3+811=1511$\frac{4}{11}+\frac{3}{11}+\frac{8}{11}=\frac{4+3+8}{11}=\frac{15}{11}$

Sum of second column = 911+511+111=9+5+111=1511$\frac{9}{11}+\frac{5}{11}+\frac{1}{11}=\frac{9+5+1}{11}=\frac{15}{11}$

Sum of third column = 211+711+611=2+7+611=1511$\frac{2}{11}+\frac{7}{11}+\frac{6}{11}=\frac{2+7+6}{11}=\frac{15}{11}$

Sum of first diagonal (left to right) = 411+511+611=4+5+611=1511$\frac{4}{11}+\frac{5}{11}+\frac{6}{11}=\frac{4+5+6}{11}=\frac{15}{11}$

Sum of second diagonal (left to right) = 211+511+811=2+5+811=1511$\frac{2}{11}+\frac{5}{11}+\frac{8}{11}=\frac{2+5+8}{11}=\frac{15}{11}$

Since, the sum of fractions in each row, in each column and along the diagonals are same, therefore, it s a magic square.

Question 4.  A rectangular sheet of paper is 1212$12\frac{1}{2}$ cm long and 1023$10\frac{2}{3}$ cm wide. Find its perimeter.

Answer: Given: The sheet of paper is in rectangular form.

Length of sheet = 1212$12\frac{1}{2}$ cm and Breadth of sheet = 1023$10\frac{2}{3}$ cm

Perimeter of rectangle = 2 (length + breadth)

= 2(1212+1023)$2\left(12\frac{1}{2}+10\frac{2}{3}\right)$ = 2(252+323)$2\left(\frac{25}{2}+\frac{32}{3}\right)$

= 2(25×3+32×26)$2\left(\frac{25\times 3+32\times 2}{6}\right)$ = 2(75+646)$2\left(\frac{75+64}{6}\right)$

= 2×