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A Pinch of History

There are instances in Rigveda where fraction has been used.
 1  3  1  1   1 
Ardhya (vèkZ)   , Tripad (f=kikn)   , Paad (ikn)   , Kushtha (oqQ"B)   12 , Kala (dyk)   16 



4
2
4

are commonly seen in Rigveda. In Sulba-sutra, Ansh (va'k)/Bhag (Hkkx) has been used as Triansh
1 1 1
(f=kva'k) or Tribhag (f=kHkkx) for , Pancham (iape) for and Dwadash (}kn'k) for .
3 5 12
There were special method to write mixed fraction as seen in Sulba-sutra like – ardhastam (vèkkZ"Ve)

 1  1 , trayastrashta (=k;L=k"V) 3 3 were common words found.
 7 2 , ardhanavam (vèkZuoe) 8 2    8 




In India, apart from Rigveda, fractions are used in Bakshali Manuscript (300 CE). Even
Brahmagupta in his book Brahma Sphuta Siddhanta, Mahavira in his book Ganita Sara Samgraha
and Sridhara in his work Trisatika given detail information, methods on Fraction.
Equivalent Fractions

Equivalent fractions are those fractions that have different
numerators and denominators but they represent the same
value. Let us take an example. Mridul, Meenal, and Maanvi
went out for lunch, and each of them had one parantha. Mridul 1 3 2 6 3 9
cut her parantha into three equal pieces and ate one-third of it. Meenal cut her parantha into 6
equal pieces and ate 2 of them. Maanvi cut her parantha into 9 equal pieces and ate 3 of them.

Do you think they ate equal pieces of their paranthas?

1 2  1 
Mridul ate of the parantha. Meenal ate of the parantha = of the parantha  .

3 6  3 
3  1  1
Maanvi ate of the parantha = of the parantha  . The value of each fraction is same which is .

9  3  3
1 2 3
Thus fractions , , represent the same fraction. These are called equivalent fractions.
3 6 9

activity
Make a fractional wall using strips which denote the same length but expressed in different fractional units.
1 Unit
1 1
2 2
1 1 1 1
4 4 4 4
1 1 1 1 1 1 1 1
8 8 8 8 8 8 8 8
1 1 1 1 1 1
Observe that two s, four s, and eight s are equal to 1. Further, two s, four s equal to .
2 4 8 4 8 2
1 2 4
Thus , , are all ‘equivalent fractions’ that denote the same length, but they all are expressed in terms of
2 4 8
different fractional units.

213 Fractions