### Fractions and Decimals - Solutions

CBSE Class –VII Mathematics

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

Question 1. Solve:

(i)2-$\frac{3}{5}$          (ii) 4 + $\frac{7}{8}$       (iii)$\frac{3}{5}+\frac{2}{7}$    (iv) $\frac{9}{11}-\frac{4}{15}$

(v)$\frac{7}{10}+\frac{2}{5}+\frac{3}{2}$    (vi)i$2\frac{2}{3}+3\frac{1}{2}$

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

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

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

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

(iv)$\frac{9}{11}-\frac{4}{15}$ = $\frac{135-44}{165}=\frac{91}{165}$

(v) $\frac{7}{10}+\frac{2}{5}+\frac{3}{2}$ = $\frac{7+4+15}{10}$ = $\frac{26}{10}=\frac{13}{5}$ = $2\frac{3}{5}$

(vi) $2\frac{2}{3}+3\frac{1}{2}$ = $\frac{8}{3}+\frac{7}{2}$ = $\frac{16+21}{6}$ = $\frac{37}{6}$ = $6\frac{1}{6}$

(vii)$8\frac{1}{2}-3\frac{5}{8}$ = $\frac{17}{2}-\frac{29}{8}$ = $\frac{68-29}{8}$ = $\frac{39}{8}$ = $4\frac{7}{8}$

Question 2. Arrange the following in descending order:

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

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

Answer: (i) $\frac{2}{9},\frac{2}{3},\frac{8}{21}$ $⇒$ $\frac{14}{63},\frac{42}{63},\frac{24}{63}$ [Converting into like fractions]

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

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

(ii) $\frac{1}{5},\frac{3}{7},\frac{7}{10}$ $⇒$$\frac{14}{70},\frac{30}{70},\frac{49}{70}$ [Converting into like fractions]

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

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

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$\frac{6}{11}$

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

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

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

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

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

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

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

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

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 $12\frac{1}{2}$ cm long and $10\frac{2}{3}$ cm wide. Find its perimeter.

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

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

Perimeter of rectangle = 2 (length + breadth)

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

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