Question

Write shaded portion as fraction. Arrange them in ascending and descending order using correct sign $<,=,>$ between the fractions:-

Answer 1

We know that a fraction is represented as $\frac{p}{q}$ where $q$ represents the whole part and $p$ represents the considered part (shaded/unshaded).

a) The circles, are divided into $8$ equal parts and hence,

Total parts = $8$

For, circle $1$, shaded part = $3$, Fraction = $\frac{3}{8}$

For, circle $2$, shaded part = $6$, Fraction = $\frac{6}{8}$

For, circle $3$, shaded part = $4$, Fraction = $\frac{4}{8}$

For, circle $4$, shaded part = $1$, Fraction = $\frac{1}{8}$

Therefore, required fractions are = $\frac{3}{8},\frac{6}{8},\frac{4}{8},\frac{1}{8}$ respectively.

Also, as,

$1<3<4<6\Rightarrow \frac{1}{8}<\frac{3}{8}<\frac{4}{8}<\frac{6}{8}$

b) The squares are divided into $9$ equal pieces, therefore,

Total parts = $9$

For, square $1$, shaded part =$8$, Fraction = $\frac{8}{9}$

For, square $2$, shaded part = $4$, Fraction = $\frac{2}{9}$

For, square $3$, shaded part = $3$, Fraction = $\frac{3}{9}$

For, square $4$, shaded part = $6$, Fraction = $\frac{6}{9}$

Therefore, required fractions are =$\frac{8}{9},\frac{4}{9},\frac{3}{9},\frac{6}{9}$ respectively

Also, as,

$3<4<6<8\Rightarrow \frac{3}{9}<\frac{4}{9}<\frac{6}{9}<\frac{8}{9}$

c) As in the given fractions, numerator is less than or equal to denominator, therefore, the fractions a re proper and hence will lie between $0$ and $1$. To do so, as the denominator is $6$, we divide the intervals from $0$ to $1$ in $6$ equal intervals and mark them on the number line as shown.

For $\frac{8}{6}$, we will further divide the interval from $1$ to $2$ in $6$ equal intervals and mark the given fraction.

Thus, fractions have been plotted.

Also, from the given number line, as numbers to the right are greater than that at the left, hence,

$\Rightarrow \frac{5}{6}>\frac{2}{6}$
$\Rightarrow \frac{3}{6}>0$
$\Rightarrow \frac{1}{6}<\frac{6}{6}$
$\Rightarrow \frac{8}{6}>\frac{5}{6}$