Chapter 4: Fractions and Decimals

Ans: We can write 0.041 as $\dfrac{{0.041}}{1}$.

So, $0.041 = \dfrac{{0.041}}{1}$

Multiply numerator and denominator by ${\mathbf{1000}}$ we have,

$0.041 = \dfrac{{0.041 \times 1000}}{{1 \times 1000}}$

$= \dfrac{{41}}{{1000}}$ 

fraction for the decimal is $\dfrac{{41}}{{1000}}$

Ans: We have, $6.03$

$6.03 = \dfrac{{603}}{{100}} = 6\dfrac{3}{{100}}$

The fraction for the decimal is $6\dfrac{3}{{100}}$

Ans: We know that,

$1{\text{Kg}} = 1000{\text{g}}$

$1{\text{g}} = \dfrac{1}{{1000}}{\text{kg}}$

$5201{\text{g}} = \dfrac{1}{{1000}} \times 5201{\text{kg}}$

$\Rightarrow 5201{\text{g}} = \dfrac{{5201}}{{1000}} = 5.201{\text{kg}}$

Ans: We know that,

1 rupee $= 100$ paisa

1 paisa $= \dfrac{1}{{100}}$ rupees

2009 paisa $= \dfrac{1}{{100}} \times 2009$ rupees

$\Rightarrow 2009$ paisa $= \dfrac{{2009}}{{100}} = 20.09$ rupees

The mixed fraction is Rs. $20\dfrac{9}{{100}}$.

Ans: We know that,

1 meter $= 100$centimeters

1 centimeter $= \dfrac{1}{{100}}$ meter

$1537{\text{cm}} = \dfrac{1}{{100}} \times 1537{\text{m}}$

$\Rightarrow 1537{\text{cm}} = \dfrac{{1537}}{{100}}{\text{m}}$

Ans: We know that

$1{\text{km}} = 1000{\text{m}}$

$1{\text{m}} = \dfrac{1}{{1000}}{\text{km}}$

$2435{\text{m}} = \dfrac{1}{{1000}} \times 2435{\text{km}}$

$2435{\text{m}} = \dfrac{{2435}}{{1000}}{\text{km}} = 2.435{\text{km}}$

Dividing numerator and denominator by $5$ we have,

$\dfrac{{2435 \div 5}}{{1000 \div 5}}{\text{km}} = \dfrac{{487}}{{200}}{\text{km}}$

By long division method quotient and reminder is $2{\kern 1pt} {\kern 1pt} \,{\text{and}}{\kern 1pt} {\kern 1pt} {\kern 1pt} 87$

The mixed fraction is $2\dfrac{{87}}{{200}}$

Ans: Given fraction is $\dfrac{2}{3},\dfrac{3}{4},\dfrac{1}{2}$ and $\dfrac{5}{6}$

Take the LCM of $3,4,2$and $6$

The ${\text{LCM}}$ of $3,4,2$and $6$ is $2 \times 2 \times 3 = 12$

${\text{Now }},\dfrac{{2 \times 4}}{{3 \times 4}} = \dfrac{8}{{12}},$

$\dfrac{{3 \times 3}}{{4 \times 3}} = \dfrac{9}{{12}}$

$\dfrac{{1 \times 6}}{{2 \times 6}} = \dfrac{6}{{12}},$

$\dfrac{{5 \times 2}}{{6 \times 2}} = \dfrac{{10}}{{12}}$ 

Now, arrange the following the ascending order

$\dfrac{6}{{12}} < \dfrac{8}{{12}} < \dfrac{9}{{12}} < \dfrac{{10}}{{12}}\quad $

The ascending order of the function is $\dfrac{1}{2} < \dfrac{2}{3} < \dfrac{3}{4} < \dfrac{5}{6}$.

Ans: The given fraction is $\dfrac{6}{7},\dfrac{7}{8},\dfrac{4}{5}$ and $\dfrac{3}{4}$

Take the LCM of $7,8,5$and $4$

The ${\text{LCM}}$ of $7,8,5$and $4 = 2 \times 2 \times 2 \times 5 \times 9 = 280$

${\text{Now, }}\dfrac{6}{7} = \dfrac{{6 \times 40}}{{7 \times 40}} = \dfrac{{240}}{{280}},$

$\dfrac{7}{8} = \dfrac{{7 \times 35}}{{8 \times 35}} = \dfrac{{245}}{{280}}$

$\dfrac{4}{5} = \dfrac{{4 \times 56}}{{5 \times 56}} = \dfrac{{224}}{{280}}{\text{ and }}\dfrac{3}{4} = \dfrac{{3 \times 70}}{{4 \times 70}} = \dfrac{{210}}{{280}}$

Now, arrange the following the descending order

$\dfrac{{245}}{{280}} > \dfrac{{240}}{{280}} > \dfrac{{224}}{{280}} > \dfrac{{210}}{{280}}$

The descending order of the fraction is $\dfrac{7}{8} > \dfrac{6}{7} > \dfrac{4}{5} > \dfrac{3}{4}$.

Ans: Given fraction $\dfrac{3}{4}$

If multiply 4 by 11 it become 44

Now,

$\dfrac{3}{4} \times \dfrac{{11}}{{11}} = \dfrac{{3 \times 11}}{{4 \times 11}} = \dfrac{{33}}{{44}}$

$\dfrac{3}{4}$ is equivalent to $\dfrac{{33}}{{44}}$

Ans: Given fraction $\dfrac{5}{6}$

If multiply $5$ by $12$ it become $60$

Now,

$\dfrac{5}{6} = \dfrac{{5 \times 12}}{{6 \times 12}}$ 

$\dfrac{5}{6} = \dfrac{{60}}{{72}}$ 

$\dfrac{5}{6}$ is equivalent to $\dfrac{{60}}{{72}}$.