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How to Simplify Large Fractions

Introduction:

 Fractions are always written in simplest form. By the term "simplest form " we mean that the only common factor for the numerator and the denominator is 1. In case when we discuss the ratio of large numbers we can still express them in their simplest form. Let us discuss some of the examples to express large numbers into their simplest form.


Simplification of Large Fractions: 

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While simplifying large fractions, we can start dividing the numerators and denominators by the common factors to arrive at the simplest form.

Example 1: $\frac{1430}{2730}$

Solution:                    

                 $\frac{1430}{2730}$ =$ \frac{1430\div 5}{2730\div 5}$

                            =$\frac{286}{546}$

                            =$\frac{286\div 2}{546\div 2}$ [ dividing the numerator and denominator by 2 ]

                           = $\frac{143}{273}$

                           =$\frac{11\times 13}{3\times 7\times 13}$ [ splitting the numerator and the denominator into prime factors ]

                         =$\frac{11}{21}$ Final Answer in the simplest form.

Example 2: $\frac{1020}{1275}$


Solution:

                 $\frac{1020}{1275}$ = $\frac{1020\div 3}{1275\div 3}$

                            = $\frac{340}{425}$

                           = $\frac{340\div 5}{425\div 5}$ [dividing the numerator and denominator by 5 ]

                          = $\frac{68}{85}$

                          = $\frac{2\times 2\times 17}{5\times 5\times 17}$ [splitting the numerator and the denominator into prime factors ] ]

                          = $\frac{4}{25}$ Final Answer in the simplest form.

Practice Questions:

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!. Simplify :$\frac{1225}{210}$

2. Simplify : $\frac{1575}{420}$