Exercise 1.4 - Chapter 1 Number Systems Term 3 7th Maths Guide Samacheer Kalvi Solutions - SaraNextGen [2024-2025]

Updated By SaraNextGen

On April 24, 2024, 11:35 AM

Ex $1.4$
Question 1.
Simplify the following
(i) $0.6 \div 3$
(ii) $0.90 \div 5$
(iii) $4.08 \div 4$
(iv) $21.56 \div 7$
(v) $0.564 \div 6$
(vi) $41.36 \div 4$
(vii) $298.2 \div 3$
Solution:
(i) $0.6 \div 3$
$=\frac{6}{10} \times \frac{1}{3}$
$=\frac{6}{3} \times \frac{1}{10}$
$=2 \times \frac{1}{10}$
$=\frac{2}{10}$
$=0.2$
(ii) $0.90 \div 5$
$=\frac{90}{100} \times \frac{1}{5}$
$=\frac{90}{5} \times \frac{1}{100}$
$=18 \times \frac{1}{100}=\frac{18}{100}$
$=0.18$
(iii) $4.08 \div 4$
$\begin{aligned}
&=\frac{408}{100} \times \frac{1}{4} \\
&=\frac{408}{4} \times \frac{1}{100}
\end{aligned}$

$\begin{aligned}
&=102 \times \frac{1}{100} \\
&=\frac{102}{100} \\
&=1.02 \\
&\text { (iv) } 21.56 \div 7 \\
&=\frac{2156}{100} \times \frac{1}{7} \\
&=\frac{2156}{7} \times \frac{1}{100} \\
&=308 \times \frac{1}{100} \\
&=\frac{308}{100} \\
&=3.08 \\
&\text { (v) } 0.564 \div 6 \\
&=\frac{564}{1000} \times \frac{1}{6} \\
&=\frac{564}{6} \times \frac{1}{1000} \\
&=\frac{94}{1000} \\
&=0.094 \\
&\text { (vi) } 41.36 \div 4 \\
&=\frac{4136}{100} \times \frac{1}{4} \\
&=\frac{4136}{4} \times \frac{1}{100} \\
&=\frac{1034}{100} \\
&=10.34 \\
&\text { (vii) } 298.2 \div 3 \\
&=\frac{2982}{10} \times \frac{1}{3} \\
&=\frac{2982}{3} \times \frac{1}{10} \\
&=\frac{994}{10}
\end{aligned}$

= 99.4

Question $2 .$
Simplify the following.
(i) $5.7 \div 10$
(ii) $93.7 \div 10$
(iii) $0.9 \div 10$
(iv) $301.301 \div 10$
(v) $0.83 \div 10$
(vi) $0.062 \div 10$
Solution:
(i) $5.7 \div 10$
$\begin{aligned}
&=\frac{57}{10} \times \frac{1}{10} \\
&=\frac{57}{100} \\
&=0.57
\end{aligned}$
(ii) $93.7 \div 10$
$\begin{aligned}
&=\frac{937}{10} \times \frac{1}{10} \\
&=\frac{937}{100} \\
&=9.37
\end{aligned}$

(iii) $0.9 \div 10$
$\begin{aligned}
&=\frac{9}{10} \times \frac{1}{10} \\
&=\frac{9}{100} \\
&=0.09
\end{aligned}$
(iv) $301.301 \div 10$
$\begin{aligned}
&=\frac{301301}{1000} \times \frac{1}{10} \\
&=\frac{30101}{10000} \\
&=30.1301 \\
&\text { (v) } 0.83 \div 10
\end{aligned}$
$\begin{aligned}
&\text { (v) } 0.83 \div 10 \\
&=\frac{83}{100} \times \frac{1}{10} \\
&=\frac{83}{1000} \\
&=0.083
\end{aligned}$
(vi) $0.062 \div 10$
$\begin{aligned}
&(v i) 0.062 \div 10 \\
&=\frac{62}{1000} \times \frac{1}{10} \\
&=\frac{62}{1000} \\
&=0.0062
\end{aligned}$

Question $3 .$
Simplify the following.
(i) $0.7 \div 100$
(ii) $3.8 \div 100$
(iii) $49.3 \div 100$
(iv) $463.85 \div 100$

(v) $0.3 \div 100$
(vi) $27.4 \div 100$
Solution:
(i) $0.7 \div 100$
$\begin{aligned}
&=\frac{7}{10} \times \frac{1}{100} \\
&=\frac{7}{1000} \\
&=0.007
\end{aligned}$
(ii) $3.8 \div 100$
$\begin{aligned}
&=\frac{38}{10} \times \frac{1}{100} \\
&=\frac{38}{1000} \\
&=0.038
\end{aligned}$
(iii) $49.3 \div 100$
$\begin{aligned}
&\text { (iii) } 49.3 \div 100 \\
&=\frac{493}{10} \times \frac{1}{100} \\
&=\frac{493}{1000} \\
&=0.493
\end{aligned}$

$\begin{aligned}
&\text { (iv) } 463.85 \div 100 \\
&=\frac{46385}{100} \times \frac{1}{100} \\
&=\frac{46385}{1000} \\
&=4.6385 \\
&\text { (v) } 0.3 \div 100 \\
&=\frac{3}{10} \times \frac{1}{100} \\
&=\frac{3}{1000} \\
&=4.6385 \\
&\text { (vi) } 27.4 \div 100 \\
&=\frac{274}{10} \times \frac{1}{100} \\
&=\frac{274}{1000} \\
&=0.274
\end{aligned}$

Question $4 .$
Simplify the following.
(i) $18.9 \div 1000$
(ii) $0.87 \div 1000$
(iii) $49.3 \div 1000$
(iv) $0.3 \div 1000$
(v) $382.4 \div 1000$
(vi) $93.8 \div 1000$

Solution:
(i) $18.9 \div 1000$
$\begin{aligned}
&=\frac{189}{10} \times \frac{1}{1000} \\
&=\frac{189}{10000} \\
&=0.0189
\end{aligned}$
(ii) $0.87 \div 1000$
$\begin{aligned}
&=\frac{87}{100} \times \frac{1}{1000} \\
&=\frac{87}{100000} \\
&=0.00087
\end{aligned}$
$\begin{aligned}
&=\frac{493}{10} \times \frac{1}{100} \\
&=\frac{493}{1000} \\
&=0.493 \\
&\text { (iv) } 0.3 \div 1000 \\
&=\frac{3}{10} \times \frac{1}{1000} \\
&=\frac{3}{10000} \\
&=0.0003 \\
&\text { (v) } 382.4 \div 1000
\end{aligned}$
$\text { (v) } 382.4 \div 1000$
$\begin{aligned}
&\text { (v) } 382.4 \div 1000 \\
&=\frac{3824}{10} \times \frac{1}{1000} \\
&=\frac{3824}{10000} \\
&=0.3824 \\
&\text { (vi) } 93.8 \div 1000 \\
&=\frac{938}{10} \times \frac{1}{1000} \\
&=\frac{938}{10000} \\
&=0.0938
\end{aligned}$

Question $5 .$
Simplify the following.
(i) $19.2 \div 2.4$
(ii) $4.95 \div 0.5$
(iii) $19.11 \div 1.3$
(iv) $0.399 \div 2.1$
(v) $5.4 \div 0.6$
(vi) $2.197 \div 1.3$
Solution:
(i) $19.2 \div 2.4$
$19.2 \div 2.4=\frac{\left(\frac{192}{10}\right)}{\left(\frac{24}{10}\right)}=\frac{192}{10} \times \frac{10}{24}=\frac{192}{24}=8$
(ii) $4.95 \div 0.5$
$4.95 \div 0.5=\frac{\left(\frac{495}{100}\right)}{\left(\frac{5}{10}\right)}=\frac{495}{100} \times \frac{10}{5}=\frac{495}{5} \times \frac{10}{100}=99 \times \frac{1}{10}=\frac{99}{10}=9.9$

(iii) $19.11 \div 1.3$
$19.11 \div 1.3=\frac{\left(\frac{19 \times 11}{100}\right)}{\left(\frac{13}{10}\right)}=\frac{1911}{100} \times \frac{10}{13}$
$=\frac{1911}{13} \times \frac{10}{100}=147 \times \frac{1}{10}=\frac{147}{10}=14.7$
(iv) $0.399 \div 2.1$
$\begin{aligned}
0.399 \div 2.1 &=\frac{\left(\frac{399}{1000}\right)}{\frac{21}{10}}=\frac{399}{1000} \times \frac{10}{21} \\
&=\frac{399}{21} \times \frac{10}{1000} \\
&=19 \times \frac{1}{100}=\frac{19}{100}=0.19
\end{aligned}$

(v) $5.4 \div 0.6$
$\begin{aligned}
5.4 \div 0.6 &=\frac{\left(\frac{54}{10}\right)}{\left(\frac{6}{10}\right)}=\frac{54}{10} \times \frac{10}{6} \\
&=\frac{54}{6}=9
\end{aligned}$
(vi) $2.197 \div 1.3$
$\begin{aligned}
2.197 \div 1.3 &=\frac{\left(\frac{2197}{1000}\right)}{\left(\frac{13}{10}\right)}=\frac{2197}{1000} \times \frac{10}{13} \\
&=169 \times \frac{1}{100} \\
&=\frac{169}{100}=1.69
\end{aligned}$

Question $6 .$
Divide $9.55 \mathrm{~kg}$ of sweet among 5 children. How much will each child get?
Solution:
Weight of the sweet $=9.55 \mathrm{Kg}$
Weight of sweet for 5 children $=\frac{955}{100} \mathrm{Kg}$
Weight of sweet for 1 child $=\frac{\left(\frac{955}{100}\right)}{5}=\frac{955}{100} \times \frac{1}{5}=\frac{955}{5} \times \frac{1}{100}$ $=\frac{191}{100}=1.91$
Each child will get $1.91 \mathrm{~kg}$ sweet.
 

Question $7 .$
A vehicle covers a distance of $76.8 \mathrm{~km}$ for $1.2$ litre of petrol. How much distance will it cover for one litre of petrol?
Solution:
For $1.2$ litre of petrol the distance covered $=76.8 \mathrm{Km}=\frac{768}{10} \mathrm{Km}$

$\therefore$ For 1, litre of petrol distance covered $=\frac{\left(\frac{768}{10}\right)}{1.2} \mathrm{~km}$
$\begin{aligned}
&=\frac{\left(\frac{768}{10}\right)}{\left(\frac{12}{10}\right)}=\frac{768}{10} \times \frac{10}{12} \\
&=\frac{768}{12} \times \frac{10}{10}=64 \mathrm{~km}
\end{aligned}$
For 1 litre of petrol distance covered $=64 \mathrm{Km}$
 

Question $8 .$
Cost of levelling a land at the rate of $₹ 15.50 \mathrm{sq}$. $\mathrm{ft}$ is $₹ 10,075$. Find the area of the land. Solution:
Cost of levelling the entire land $=₹ 10,075$
Cost of levelling $1 \mathrm{sq}$. $\mathrm{ft}=₹ 15.50$
$\therefore$ Area of the land $=\frac{\text { Cost of levelling entire land }}{\text { Cost of levelling } 1 \mathrm{sq} . \mathrm{ft} .}$
$\begin{aligned}
&=\frac{10075}{15.50} \times \frac{100}{100}=\frac{10075 \times 100}{15.50 \times 100}=\frac{1007500}{1550} \\
&=\frac{100750}{155}=650
\end{aligned}$
$\therefore$ Area of the land $=650 \mathrm{sq} . \mathrm{ft}$.

Question $9 .$
The cost of 28 books are $₹ 1506.4$. Find the cost of one book.
Solution:
Cost of 28 books $=₹ 1506.4$
Cost of 1 book $=\frac{1506.4}{28}=\frac{\frac{15064}{\frac{10}{28}}}{\frac{1}{1}}=\frac{15064}{10} \times \frac{1}{28}$
$=\frac{15064}{28} \times \frac{1}{10}=538 \times \frac{1}{10}=\frac{538}{10}=₹ 53.80$
Cost of 1 book $=₹ 53.80$

Question $10 .$
The product of two numbers is $40.376$. One number is $14.42$. Find the other number. Product of two numbers $=40.376$
One number $=14.42$

$\begin{aligned}
\text { Another number } &=\frac{40.376}{14.42}=\frac{\frac{40376}{1000}}{\frac{1442}{100}} \\
&=\frac{40376}{1000} \times \frac{100}{1442}=\frac{40376}{1442} \times \frac{100}{1000} \\
&=28 \times \frac{1}{10}=\frac{28}{10}=2.8 \\
\text { Other number } &=2.8
\end{aligned}$

Objective Type Questions
Question $1 .$
$5.6 \div 0.5=$ ?
(i) $11.4$
(ii) $10.4$
(iii) $0.14$
(iv) $11.2$
Answer:
(iv) $11.2$
Hint:
$\frac{5.6}{0.5}=\frac{56}{5}$
$=11.2$

Question $2 .$
$2.01 \div 0.03=$ ?
(i) $6.7$
(ii) $67.0$
(iii) $0.67$
(iv) $0.067$
Answer:
(ii) $67.0$
Hint: $\frac{2.01}{0.03}=\frac{201}{3}$ $=67$

Question $3 .$
$0.05 \div 0.5=$ ?
(i) $0.01$
(ii) $0.1$
(iii) $0.10$
(iv) $1.0$
Answer:
(ii) $0.1$