The factor trees find the prime factorizations. The prime factorizations find the GCF. The GCF simplifies the fraction.
150
75,2
25,3,2
5,5,3,2
225
75,3
25,3,3
5,5,3,3
The GCF is 75
150/225 = 2/3
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Divide both by their highest common factor.
Put .38 over 100 to get 38/100. Simplify the fraction using the greatest common factor to get 19/50.
The same way you simplify any fraction: 1) Look for common factors between the two numbers. 2) If you find one, divide both numbers by that factor.
Because 3 and 9 are both divisible by 3, we can simplify this fraction into 1/3.
3 over 4