question_answer

Draw the number line and represent the following rational number on it.

(a) \[\frac{3}{4}\]

(b) \[\frac{-5}{8}\]

(c) \[\frac{-7}{4}\]

(d) \[\frac{7}{8}\]

Answer:

(a) Firstly, draw a number line and 0, 1 at unit distance, divide the gap between 0 and 1 into 4 equal parts and show 1 part as \[\frac{1}{4}\] .

Now, \[\frac{3}{4}\] means 3 parts out of 4 parts to the right of 0. Thus, point A on the number line represents the rational number \[\frac{3}{4}\] as shown below:

(b) Here, \[\frac{-5}{8}\] is less than 0 and greater than -1. So, it will lie on the left of 0 on the number line at the same distance as \[\frac{5}{8}\] from 0 to the right.

Firstly, draw the number line and mark 0, -1 on it at unit distance divide the gap between 0 and -1 into 8 equal parts and show 1 part, as \[\frac{-1}{8}\],

Now, \[\frac{-5}{8}\] means 5 parts out of 8 parts to the left of 0.

Thus, point B on the number line represents the rational number \[\frac{-5}{8}\]as shown below.

(c)Here, \[\frac{-7}{4}\] is greater than-2 and less then-I, so it will lie between -2 and -1 to the left of 0 at the same distance as \[\frac{7}{4}\] from 0 to the right.

Firstly, draw the number line and mark 0, -1, -2 on it at unit distance. Divide the gap between 0, -1, -2 into 4 equal parts and show 1 part as \[\frac{1}{4}\].

Now, \[\frac{7}{4}\]\[=-\left( 1+\frac{3}{4} \right)\]means 1 unit distance and 3 parts out of 4 parts (between --1 and - 2) to the left of zero.

(d) Similarly ? can be represented as