Chapter 4: Fractions and Decimals

Ans: $\dfrac{{18}}{{135}}$ and $\dfrac{{90}}{{675}}$ Are proper, unlike and equivalent fractions.

Ans: Given fraction is 

  $8\dfrac{7}{2} = \dfrac{{(8 \times 7) + 7}}{2}$

  $= \dfrac{{56 + 2}}{7}$

   $= \dfrac{{58}}{7}$ 

$8\dfrac{2}{7}$ Is equal to the improper fraction $\dfrac{{58}}{7}$

Ans: By long division the quotient and reminder will be $12\,\,{\kern 1pt} {\text{and}}{\kern 1pt} \,{\kern 1pt} 3$

 $\dfrac{{87}}{7}$ Is equal to the mixed fraction $12\dfrac{3}{7}$

Ans: The LCM of $10$ and $100$ is$100$.

Hence, $9 + \dfrac{2}{{10}} + \dfrac{6}{{100}}$

$= \dfrac{{9 \times 100 + 2 \times 10 + 6}}{{100}}$

$\Rightarrow \dfrac{{962}}{{100}} = 9.26$

Ans: Now, $16.25$

$\Rightarrow \dfrac{{1625}}{{100}} = \dfrac{{1625 \div 25}}{{100 \div 25}} = \dfrac{{65}}{4}$

Decimal $16.25$are equal to the fraction $\dfrac{{65}}{4}$.

Ans: Given fraction is 

  $\dfrac{7}{{25}} = \dfrac{{7 \times 4}}{{25 \times 4}}$

   $= \dfrac{{28}}{{100}}$

   $= 0.28$ 

fraction $\dfrac{7}{{25}}$ is equal to the decimal number $0.28$

Ans: Explanation,

For the fractions denominator is same so add only numerator

$\Rightarrow \dfrac{{17}}{9} + \dfrac{{41}}{9} = \dfrac{{17 + 41}}{9} = \dfrac{{58}}{9}$

So,

$\dfrac{{17}}{9} + \dfrac{{41}}{9} = \dfrac{{58}}{9}$

Ans: Explanation,

For the fractions denominator is same so subtract only numerator

$\Rightarrow \dfrac{{67}}{{14}} - \dfrac{{24}}{{14}} = \dfrac{{67 - 24}}{{14}} = \dfrac{{43}}{{14}}$

Hence,

$\dfrac{{67}}{{14}} - \dfrac{{24}}{{14}} = \dfrac{{43}}{{14}}$

Ans: Explanation,

Rewrite the mixed fraction and add the numerator

$\Rightarrow \dfrac{{17}}{2} + 3\dfrac{1}{2} = \dfrac{{17}}{2} + \dfrac{7}{2} = \dfrac{{17 + 7}}{2}$

$\Rightarrow \dfrac{{24}}{2} = \dfrac{{24 \div 2}}{{2 \div 2}} = 12$

Hence, $\dfrac{{17}}{2} + 3\dfrac{1}{2} = 12$

Ans: Explanation,

Rewrite the mixed fraction and subtract the numerator

   $\Rightarrow 9\dfrac{1}{4} - \dfrac{5}{4} = \dfrac{{37}}{4} - \dfrac{5}{4}$

   $= \dfrac{{37 - 5}}{4} = \dfrac{{32}}{4}$

   $\Rightarrow \dfrac{{32 \div 4}}{{4 \div 4}} = 8$ 

Therefore, $9\dfrac{1}{4} - \dfrac{5}{4} = 8$