Conversion of a Fraction into its Smallest and Simplest Form
In conversion of a fraction into its smallest and simplest form are discussed here.
If the numerator and denominator of a fraction have no common factors
then the fraction is considered as its smallest and simplest form, as 3/5, 2/3, 4/7, 7/11, etc., are the simplest forms of 6/10, 8/12, 20/35, 21/33 respectively.
Examples on conversion of a fraction into its smallest and simplest form:
1. Change 45/60 to its simplest form.
Solution:
All the factors of numerator and denominator are written;
45 = 3 x 3 x 5 and 60 = 3 x 2 x 2 x 5 (common factors are removed)
= 3/4
Thus, to get the simplest form of a fraction, the common factors of numerator and denominator are removed.
2. Change 15/75 to its simplest form.
Solution:
All the factors of numerator and denominator are written
15 = 3 x 5 and 75 = 3 x 5 x 5 (common factors are removed)
= 1/5
Thus, to get the simplest form of a fraction, the common factors of numerator and denominator are removed.
Reducing Fraction to the Lowest Term:
You have learnt to find equivalent fractions by multiplying and diving.
Now let us try to reduce fractions to the lowest term.
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Equivalent fraction in the lowest term.
2. Sometimes we need to divide more than once.
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So, 16/24 = 2/3
Therefore, 2/3 is the lowest term
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We have divided by the highest common factor
Note:
When the numerator and the denominator of the fraction cannot be
divided by a factor greater than 1, the fraction is in its lowest term.
For example, 3/4, 2/3, 1/2
Related Concept
● Representation of a Fraction
● Properties of Equivalent Fractions
● Comparison of Like Fractions
● Comparison of Fractions having the same Numerator
● Conversion of Fractions into Fractions having Same Denominator
● Conversion of a Fraction into its Smallest and Simplest Form
● Addition of Fractions having the Same Denominator
● Subtraction of Fractions having the Same Denominator
● Addition and Subtraction of Fractions on the Fraction Number Line
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