Fill in the following blanks:

(i) A fraction is a number which represent a ….. of whole.

(ii) A proper fraction lies between 0 and …..

(iii) A mixed fraction can be converted into ….. fraction.

(iv) Fractions having different denominators are called …..

(v) $\dfrac{18}{135}$ and $\dfrac{72}{540}$ are proper, unlike and …… fractions.

(vi) In two like fractions, the fraction having smaller numerator is …..

(vii) $\dfrac{144}{180}$ reduced to simplest form is …..

(viii) $7\dfrac{2}{5}$ + …. = 12

(ix) $\dfrac{42}{56} = \dfrac{6}{…}$

(i) A fraction is a number which represent a part of whole.

(ii) A proper fraction lies between 0 and 1.

(iii) A mixed fraction can be converted into an improper fraction.

(iv) Fractions having different denominators are called unlike fractions.

(v) Check by cross multiplication: 18 × 540 = 9720 and 135 × 72 = 9720.

Since cross products are equal, the fractions are equivalent.

So, $\dfrac{18}{135}$ and $\dfrac{72}{540}$ are proper, unlike and equivalent fractions.

(vi) In two like fractions, the fraction having smaller numerator is smaller.

(vii) $\dfrac{144}{180}$

By prime factorisation,

$\Rightarrow \dfrac{144}{180} = \dfrac{2 \times 2 \times 2 \times 2 \times 3 \times 3}{2 \times 2 \times 3 \times 3 \times 5}\\[1em] = \dfrac{2 \times 2}{5} \\[1em] = \dfrac{4}{5}.$

So, $\dfrac{144}{180}$ reduced to simplest form is $\dfrac{4}{5}$.

(viii) $7\dfrac{2}{5}$ + …. = 12

Required number = $12 - 7\dfrac{2}{5} = \dfrac{12}{1} - \dfrac{37}{5} = \dfrac{60}{5} - \dfrac{37}{5} = \dfrac{60 - 37}{5} = \dfrac{23}{5} = 4\dfrac{3}{5}$.

So, $7\dfrac{2}{5}$ + $4\dfrac{3}{5}$ = 12.

(ix) $\dfrac{42}{56} = \dfrac{6}{…}$

To get 6 from 42, we have to divide 42 by 7. So, divide 56 by 7.

$\dfrac{42}{56} = \dfrac{42 \div 7}{56 \div 7} = \dfrac{6}{8}$.

So, $\dfrac{42}{56} = \dfrac{6}{\textbf{8}}$.