When the numerator and denominator have only 1 as a common factor
Yeah, that tends to happen sometimes.
When a fraction is reduced, or simplified, fraction.
A fraction in which the greatest common factor of the numerator and the denominator is 1 is a reduced, or simplified, fraction.
For example:
6 / 8 is not reduced (or not simplified) because 6 / 8 = 2 ∙ 3 / 2 ∙ 4 = 3 / 4
3 / 4 is a reduced, or simplified, fraction.
Also 6 / 7 , 12 / 5 , 19 / 14 etc. is a reduced, or simplified, fractions.
You can use prime factorization ( if you know what it is ) to reduce fractions.
form all quotient that have factors of 1 in the numerator and factors of 2 in the numerator
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When the numerator and denominator have only 1 as a common factor, it means that the numerator and denominator do not share any other common factors apart from 1.
To determine if 1 is the only common factor, you need to find the factors of both the numerator and the denominator. Factors are the numbers that evenly divide another number. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.
If, after finding the factors of the numerator and denominator, you find that the only factor they share is 1, then the numerator and denominator have only 1 as a common factor.
Here's an example:
Let's say you have the fraction 8/12.
The factors for the numerator, 8, are 1, 2, 4, and 8.
The factors for the denominator, 12, are 1, 2, 3, 4, 6, and 12.
In this case, the common factors between 8 and 12 are 1 and 2. Since the numerator and denominator have factors other than 1, 1 is not the only common factor.
However, if you have a fraction like 7/11, the factors for 7 are 1 and 7, while the factors for 11 are 1 and 11. The only common factor between 7 and 11 is 1. Therefore, the numerator and denominator have only 1 as a common factor.
So, when the numerator and denominator have only 1 as a common factor, it means that no other number apart from 1 can divide both the numerator and denominator evenly.