S.chand publication New Learning Composite mathematics solution of class 7 Chapter 2 Fractions and Decimals Exercise 2F

 Exercise 2F

Question 1

Simplify and express your answers in simplest form and mixed numbers.

(a) $1\frac{1}{4} \times \frac{2}{3} \div \frac{1}{6}$

$=\frac{5}{4} \times \frac{2}{3} \times \frac{6}{1}$

=5

(b) $1\frac{1}{2} \div \left(\frac{1}{4}\times \frac{2}{3}\right)$

Sol :

$=\frac{3}{2}\div \left(\frac{1}{24} \times \frac{2}{3}\right)$

$=\frac{3}{2} \div \frac{1}{6}$

$=\frac{8}{2} \times \frac{6}{1}$

=9

(c) $16 \div \frac{1}{4} \div 4$

$=16\times \frac{4}{1}\times \frac{1}{4}$

=16

(d) $\frac{5}{8} \div 3\times 6$

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

$=\frac{5}{4}=1\frac{1}{4}$

(e) $\frac{3}{8}\times 3 -\frac{1}{8}+\frac{2}{3}$

$=\frac{9}{8}-\frac{1}{8}+\frac{2}{3}$

$=\frac{27-3+16}{24}$

$=\frac{40}{24}=\frac{5}{3}=1\frac{2}{3}$

(f) $6\frac{1}{4}\div \frac{5}{8} \div \frac{5}{2} +1$

$=\frac{25}{4} \times \frac{8}{5} \times \frac{2}{5}+1$

=4+1=5

(g) $1\frac{1}{4} \times 7 \div \left(12\frac{7}{12} -11\frac{1}{3}\right)$

$=\frac{5}{4}\times 7 \div \left(\frac{151}{12}- \frac{34}{3}\right)$

$=\frac{5}{4} \times 7 \div \left(\frac{151-136}{12}\right)$

$=\frac{5}{4} \times 7\times \frac{12}{15}$

=7

Question 2

The expression $\frac{1}{2}+\left\{4 \frac{3}{4}-\left(3 \frac{1}{6}-2 \frac{1}{3}\right)\right\}$ is equal to

(a) $3 \frac{2}{3}$

(b) $1 \frac{1}{4}$

(c) $4 \frac{5}{12}$

(d) $1 \frac{2}{3}$

Sol :

$\frac{1}{2} \left\{4\frac{3}{4}-\left(3\frac{1}{6}-2\frac{1}{3}\right)\right\}$

$=\frac{1}{2}+\left\{\frac{19}{4}-\left(\frac{19}{6}-\frac{7}{3}\right)\right\}$

$=\frac{1}{2}+\left\{\frac{19}{4}-\left(\frac{19-14}{6}\right)\right\}$

$=\frac{1}{2}+\left\{\frac{19}{4}-\frac{5}{6}\right\}$

$=\frac{1}{2}+\left\{\frac{15-10}{12}\right\}$

$=\frac{1}{2}+\frac{147}{12}$

$=\frac{6+47}{12}=\frac{53}{12}=4\frac{5}{12}$

Question 3

The value of $\left[3 \frac{1}{4} \div\left\{1 \frac{1}{4}-\frac{1}{2}\left(2 \frac{1}{2}-\frac{1}{4}-\frac{1}{6}\right)\right\}\right] \div\left(\frac{1}{2}\right.$ of $\left.4 \frac{1}{3}\right)$ is

(a) 18

(b) 36

(c) 39

(d) 78

Sol :

$=\left[ \frac{13}{4} \div \left\{\frac{5}{4}-\frac{1}{2}\left(\frac{5}{2}-\frac{1}{4}-\frac{1}{6}\right)\right\}\right]\div \left(\frac{1}{2} \times \frac{13}{3}\right)$

$=\left[ \frac{13}{4} \div \left\{\frac{5}{4}-\frac{1}{2}\left(\frac{5}{2}-\frac{3-2}{12}\right)\right\}\right]\div \left(\frac{1}{2} \times \frac{13}{3}\right)$

$=\left[ \frac{13}{4} \div \left\{\frac{5}{4}-\frac{1}{2}\left(\frac{5}{2}-\frac{1}{12}\right)\right\}\right]\div \left(\frac{1}{2} \times \frac{13}{3}\right)$

$=\left[ \frac{13}{4} \div \left\{\frac{5}{4}-\frac{1}{2}\left(\frac{30-1}{12}\right)\right\}\right]\div \left(\frac{1}{2} \times \frac{13}{3}\right)$

$=\left[ \frac{13}{4} \div \left\{\frac{5}{4}-\frac{1}{2} \times \frac{29}{12}\right\}\right]\div \left(\frac{13}{6}\right)$

$=\left[ \frac{13}{4} \div \left\{\frac{5}{4}-\frac{29}{24}\right\}\right]\div \left(\frac{13}{6}\right)$

$=\left[ \frac{13}{4} \div \left\{\frac{30-29}{24}\right\}\right]\div \left(\frac{13}{6}\right)$

$=\left[\frac{13}{4} \div \frac{1}{24}\right] \div \frac{13}{6}$

$=\left[\frac{13}{4} \times \frac{24}{1}\right] \div \frac{13}{6}$

$=78\times \frac{6}{13}$

=36