FRACTIONS ON A NUMBER LINE

Example 1 :

Represent the fraction 3/8 on a number line.

Solution :

To represent the fraction 3/8 on a number line, we can take the section from 0 to 1 and divide it up into 8 pieces, because the denominator of the fraction 3/8, that is, the whole is divided into 8 pieces.

Now, mark 3/8 at the end of the third piece from 0.

Example 2 :

Represent the fraction 11/12 on a number line.

Solution :

To represent the fraction 11/12 on a number line, we can take the section from 0 to 1 and divide it up into 11 pieces, because the denominator of the fraction 11/12, that is, the whole is divided into 11 pieces.

Now, mark 11/12 at the end of the eleventh piece from 0.

Example 3 :

Represent the fraction 7/10 on a number line.

Solution :

To represent the fraction 7/10 on a number line, we can take the section from 0 to 1 and divide it up into 10 pieces, because the denominator of the fraction 7/10, that is, the whole is divided into 10 pieces.

Now, mark 7/10 at the end of the seventh piece from 0.

Example 4 :

Draw a number line and represent the following fractions on it.

(i) 9/4   (ii) -8/3   (iii) -12/(-5)   (iv) -15/4

Solution :

Convert the given fractions to decimal numbers and represent them on a number line.

(i) 9/4 = 2.25

(ii) -8/3 = -2.66

(iii) -12/(-5) = 3.4

(iv) -15/4 = 3.75

Identifying Fractions on a Number Line

Example 5 :

Find the fraction for the question mark marked on the number line.

Solution :

The part lies between -4 and -3 is divided into three equal intervals.

Moving from -3 to the indicated arrow, we have to cover 2/3 interval.

  =  -3 + (-2/3)

  =  -11/3

So, the question mark on the number line represents -11/3.

Example 6 :

Find the fraction for the question mark marked on the number line.

Solution :

The portion between 0 and -1 is divided into 5 equal parts. Moving from 0 to the arrow indicated, we have to cover 2/5 part. Since we move to the left side, we have to take negative sign.

So, the question mark on the number line represents -2/5.

Example 7 :

Find the fraction for the question mark marked on the number line.

Solution :

The portion between 0 and -1 is divided into 4 equal parts. Moving from 1 to the arrow indicated, we have to cover 3/4 part. Since we move to the right side, we have to take positive sign.

  =  1 +  (3/4)

  =  7/4

So, the question mark on the number line represents 7/4.

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