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4. Find of the following.
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(a) 12 notebooks (b) 24 mangoes (c) 30 toffees
5. Express the following as a fraction:
(a) 11 hours of a day (b) three kiwis from eight kiwis

(c) 15 days of the month of December (d) `71 of a 100-rupee note
6. A bag contains 12 white balls and 17 black balls. What is the fraction of black balls in the bag?

Representation of Fractions on a Number Line

We have already learnt representation of whole numbers on a number line.
Let us learn how fractions are represented on the number line.

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Step 1: Draw a number line as shown below to represent a fraction say, on it.
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0 1 2 3 4 5
2
Step 2: Since is less than 1, so it lies between 0 and 1 on the number line.
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Step 3: Divide the distance between 0 and 1 into 3 equal parts as the denominator of the fraction is 3.

0 1 2 3 4 5

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Step 4: Count 2 parts starting from 0 as the numerator of the fraction is 2. Mark the fraction at
2 3
that point. Observe that the length of the red line is units.
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0 1 2 3 4 5
2
3
So, we have seen that in order to represent a fraction on the number line, we need to divide the
distance between two whole numbers as many equal parts as the denominator of the given fraction.
1 2 3 4
Similarly, we can represent , , , , etc. on a number line. 0 5
5 5 5 5 Note: 5 =0 and = 1
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Types of Fractions

Proper Fractions: A fraction whose numerator is smaller than its denominator is called a proper
fraction.
1 7 12
For example, , , , etc. are all proper fractions.
5 9 17
Unit Fractions: A fraction with numerator 1 is called a unit fraction.
1 1 1
For example, , , , etc. are all unit fractions.
3 4 7 Note: l The proper fractions are always
Improper Fractions: A fraction whose numerator is smaller than 1 and hence it always lies
between 0 and 1 on the number line.
greater than or equal to its denominator is called an l The improper fractions are always
improper fraction. equal to or greater than 1 and hence
5 9 11 7 they always lie on 1 or to the right
For example, , , , , etc. are all improper fractions. of 1 on the number line.
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209 Fractions