Draw number lines and locate the points on them: (a) (b) (c)
(a)
Step 1. Draw a line and locate the points .
First, make the same denominator in all the fractions.
Now, the points are .
Draw a number line, mark two points and on it:
Divide the gap between and into four equal parts because denominator is :
Now, first part will show , second part show third part show and last part show .
Hence, and represent and respectively.
(b)
Step 2. Draw a line and locate the points .
Draw a number line, mark two points and on it:
Divide the gap between and into eight equal parts because denominator is :
Now, first part will show . Also, second part show third part show , fourth part show , fifth part show , sixth part show , seventh part show and last part show .
Hence, and represent and respectively.
(c)
Step 3. Draw a line and locate the points ..
Draw a number line, mark two points and on it:
Divide the gap between and and between and into five equal parts because denominator is :
Now, first part will show . Also, second part show third part show , fourth part show , fifth part show , sixth part show , seventh part show , eighth part show , nineth part show , and last part show .
Hence, and represent and respectively.