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Fraction Puzzles

Introduction to fraction puzzles:

Fraction: The fraction a/b, where a and b are positive integers, was historically obtained by dividing a unit length into b parts and taking a of these parts. The number a is the numerator and the number b is the denominator. It is a proper fraction if a<b and improper fraction if a>b. Any fraction can be expressed as c+d/e, where c is an integer and d/e is a proper fraction, and in this form it is called a mixed fraction. 

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Some examples of fraction puzzles:


    1/5 = 1 part out of 5


         ¾ = 3 out of 4




Fraction shaded

Fraction remaining






One whole






2 equal parts







3 equal parts





         0                            1/3                             2/3                        

Bigger and Smaller Fractions puzzles

Bigger1                        Fraction2  

1/4                                <!--[if !vml]--><!--[endif]-->3/4

Comparing the shaded portion of the two fractions, we can say that

‘    1/ 4 <3/ 4  or 3/4 >1/4

If the denominators of the fractions are equal, the fraction with the larger numerator is bigger.

If the numerator of the fractions are equal then the fraction with the smaller denominator is the bigger fraction.


Distinguish between the below items

a) (a)                                                                           1/4   >  1/ 8

b) (b)                                                                            1/5   >  1/7

c) (c)                                                                           1/7   >  1/9

 (d)                                                                1/9   <  1/3

Write the fractions and put the correct sign <, >, =.

Fraction2                      Fraction3

Ascending and Descending order of Fractions

Wehave already seen that when the denominator of the fractions are the same the bigger fraction has the larger numerator and if the numerators are the same, the bigger fraction has the smaller denominator.


























Comparing the numerators


Therefore  1/5 < 2/5 <3/5 < 4/5

Ascending order is equals to

1/5, 2/5, 3/5, 4/5

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Examples of equivalent fractions

Fraction4           Fraction5            Fraction6

                                               1/2                                               2/4                                                           4/8

All the circles are of same size. The shaded portion in each figure are also equal. Hence we say that

1/2 = 2/4 = 4/8

These are called equivalent fraction.

If  wemultiply the numerator and denominator of a fraction by the same numberexcept 0 the value does not change. If we divide the numerator and denominator of a fraction by the same number except 0, the value does not change.