Fractions — Exercise 4(H)

Represent each of the following on the number line :

$\dfrac{2}{3}$

Answer

Draw a line. Take a point O in the middle. From O, set off equal distances on right as well as on the left. Mark them, as shown. Now, distance OA = 1 unit.

Divide OA into 3 equal parts. Take 2 parts out of it to reach the point P.

This point P represents $\dfrac{2}{3}$ on the number line.

Represent each of the following on the number line :

$\dfrac{5}{8}$

Answer

Draw a line. Take a point O in the middle. From O, set off equal distances on right as well as on the left. Mark them, as shown. Now, distance OA = 1 unit.

Divide OA into 8 equal parts. Take 5 parts out of it to reach the point P.

This point P represents $\dfrac{5}{8}$ on the number line.

Represent each of the following on the number line :

$\dfrac{1}{2}$

Answer

Draw a line. Take a point O in the middle. From O, set off equal distances on right as well as on the left. Mark them, as shown. Now, distance OA = 1 unit.

Divide OA into 2 equal parts. Take 1 part out of it to reach the point P.

This point P represents $\dfrac{1}{2}$ on the number line.

Represent each of the following on the number line :

$3\dfrac{3}{4}$

Answer

Let O be the origin. Set off equal distances OA, AB, BC, etc., on right hand side of O, denoting 1, 2, 3, etc.

Take 3 full distances and divide CD into 4 equal parts and take 3 parts out of it to reach the point P.

Hence, the point P represents $3\dfrac{3}{4}$.

Represent each of the following on the number line :

$1\dfrac{4}{7}$

Answer

Let O be the origin. Set off equal distances OA, AB, BC, etc., on right hand side of O, denoting 1, 2, 3, etc.

Take 1 full distance and divide AB into 7 equal parts. Then, take 4 parts out of it to reach point P.

Hence, the point P represents $1\dfrac{4}{7}$.

Represent each of the following on the number line :

$2\dfrac{2}{5}$

Answer

Let O be the origin. Set off equal distances OA, AB, BC, etc., on right hand side of O, denoting 1, 2, 3, etc.

Take 2 full distances and divide BC into 5 equal parts and take 2 parts out of it to reach the point P.

Hence, the point P represents $2\dfrac{2}{5}$.

Represent each of the following on the number line :

$\dfrac{1}{2} + \dfrac{1}{4}$

Answer

We know that the L.C.M. of 2 and 4 is 4.

Now, $\dfrac{1}{2} = \dfrac{2}{4}$ and $\dfrac{1}{4} = \dfrac{1}{4}$.

Divide the unit length OA from 0 to 1 into 4 equal parts. Then, each part represents $\dfrac{1}{4}$.

From 0 move 2 steps to the the right and then 1 step to the right to reach $\dfrac{3}{4}$.

$\therefore \dfrac{1}{2} + \dfrac{1}{4} = \dfrac{2}{4} + \dfrac{1}{4} = \dfrac{3}{4}$, as shown below.

Represent each of the following on the number line :

$\dfrac{1}{3} + \dfrac{1}{4}$

Answer

We know that the L.C.M. of 3 and 4 is 12.

Now, $\dfrac{1}{3} = \dfrac{4}{12}$ and $\dfrac{1}{4} = \dfrac{3}{12}$

Divide the unit length OA from 0 to 1 into 12 equal parts. Then, each part represents $\dfrac{1}{12}$.

From 0 move 4 steps to the the right and then 3 steps to the right to reach $\dfrac{7}{12}$.

$\therefore \dfrac{1}{3} + \dfrac{1}{4} = \dfrac{4}{12} + \dfrac{3}{12} = \dfrac{7}{12}$, as shown below.

Represent each of the following on the number line :

$\dfrac{5}{6} - \dfrac{1}{6}$

Answer

Divide the unit length OA from 0 to 1 into 6 equal parts. Then, each part represents $\dfrac{1}{6}$.

From 0 move 5 steps to the the right and then 1 step to the left to reach $\dfrac{4}{6}$.

$\therefore \dfrac{5}{6} - \dfrac{1}{6} = \dfrac{4}{6}$, as shown below.

Represent each of the following on the number line :

$\dfrac{4}{9} - \dfrac{2}{9}$

Answer

Divide the unit length OA from 0 to 1 into 9 equal parts. Then, each part represents $\dfrac{1}{9}$.

From 0 move 4 steps to the the right and then 2 steps to the left to reach $\dfrac{2}{9}$.

$\therefore \dfrac{4}{9} - \dfrac{2}{9} = \dfrac{2}{9}$, as shown below.