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Find:
$(i).\ 7 \div 3.5$
$(ii).\ 36 \div 0.2$
$(iii).\ 3.25 \div 0.5$
$(iv).\ 30.94 \div 0.7$
$(v).\ 0.5 \div 0.25$
$(vi).\ 7.75 \div 0.25$
$(vii).\ 76.5 \div 0.15$
$(viii).\ 37.8 \div 1.4$
$(ix).\ 2.73 \div 1.3$
To do:
We have to find
(i) $7 \div 3.5$
(ii) $36 \div 0.2$
(iii) $3.25 \div 0.5$
(iv) $30.94 \div 0.7$
(v) $0.5 \div 0.25$
(vi) $7.75 \div 0.25$
(vii) $76.5 \div 0.15$
(viii) $37.8 \div 1.4$
(ix) $2.73 \div 1.3$
Solution:
We know that,
On dividing a decimal by $10^n$, the decimal point shifts to the left by $n$ places.
$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$
Therefore,
(i) $7 \div3.5=7\times\frac{1}{3.5}$
$=7\times\frac{10}{35}$
$=\frac{70}{35}$
$=\frac{2}{1}$
$=2$
(ii) $36 \div0.2=36\times\frac{1}{0.2}$
$=36\times\frac{10}{2}$
$=\frac{360}{2}$
$=180$
(iii) $3.25 \div0.5=3.25\times\frac{1}{0.5}$
$=3.25\times\frac{10}{5}$
$=3.25\times2$
$=6.5$
(iv) $30.94 \div0.7=\frac{3094}{100}\times\frac{1}{0.7}$
$=\frac{3094}{100}\times\frac{10}{7}$
$=\frac{3094}{70}$
$=44.2$
(v) $0.5 \div0.25=\frac{5}{10}\times\frac{1}{0.25}$
$=\frac{5}{10}\times\frac{100}{25}$
$=\frac{50}{25}$
$=2$
(vi) $7.75\div0.25=\frac{775}{100} \times \frac{1}{0.25}$
$=\frac{775}{100}\times\frac{100}{25}$
$=\frac{775}{25}$
$=31$
(vii) $76.5 \div0.15=76.5\times\frac{1}{0.15}$
$=\frac{7650}{15}$
$=510$
(viii) $37.8 \div1.4=37.8\times\frac{1}{1.4}$
$=\frac{378}{10}\times\frac{10}{14}$
$=\frac{378}{14}$
$=27$
(ix) $2.73 \div1.3=\frac{273}{100}\times\frac{10}{13}$
$=\frac{21}{10}$
$=2.1$