Generating Fraction – What is it? Simple method | How to find the Generative Fraction?
Every Generative Fraction is obtained by a periodic decimal and to teach you better about the Generative Fraction, we will cover the following points: Simple Periodic Decimal, Non-Periodic Decimate and Decimal.
Simple Periodic Decimal
The Simple Periodic Decimal is the repetition of numerical terms after the decimal point, these terms determine the period, for example:
1.3333 period equals 3
0.515151 period equals 51
2.321321 period equals 321
Non-Periodic Tithe
The non-periodic decimal does not contain the repetition of terms, so it is not possible to identify a period, for example:
1.2435 there is no period
0.5432 there is no period
3.3456 there is no period
Tithe
The decimal is a fraction that does not result in an exact result, generating results with many decimal places, for example:
2,2345
1,2222
0,2323
How to find the Generative Fraction?
As we have already reminded you a little about decimals, simple periodic decimals and non-periodic decimals, it is time for you to learn how to how to find the Generative Fraction Using these points we covered, this way we are going to teach you is a simpler way, so pay close attention to the steps.
As a first step you must find the period of the periodic decimal, in this case 1.333 and the period of this periodic decimal is equal to 3.
Now you must start assembly of the Generating Fraction, the denominator will be the number 9, remembering that you must always add the number 9 as the denominator, in all cases where the numbers are repeated.
Now comes the differentiated method, we have 1.333, we must take the first number which is 1 and the first number that is repeated, which in this case is 3, so we have 13 and now we must subtract by the only number that is not repeated, which in this case is 1, so we have 13 –1 = 12.
Now we have 12 as the numerator and 9 as the denominator in the fraction, but we can still simplify by 3 and finally we will have a numerator of 4 and a denominator of 3, this is the generating fraction.
1,333
13 – 1 = 12 ÷ 3 = 4
9 ÷ 3 = 3
To check if your calculation is correct, just divide 4 by 3 and it will be 1.333.
Example 1 of Generating Fraction
We will include some examples of Generative Fraction here so you can learn how to do this calculation.
11,444
114 – 11 = 103
9
Example 2 of Generating Fraction
Let's go to example 2 of Generative Fraction, in this one we will make it a little more difficult.
1,9191
191 – 1 = 190
99
Want to check the results? Just divide the top number by the bottom number, if it gives the Periodic Decimal, which in this case is 1.9191, your calculation is correct.
Generative Fraction Exercises for you to do at home
A) 1.120120
B) 1.0101
C) 21,999
D) 12.5959
E) 2.333
Results of Generative Fraction Exercises
A) A: 373
333
B) A: 100
99
C) A: 66
3
D) A: 1247
99
E) A: 21
9
