A proper fraction is a fraction where the numerator is less than the denominator. In this case, all proper fractions with a denominator of 3 would have a numerator less than 3. Therefore, the proper fractions with a denominator of 3 would be 1/3 and 2/3. These fractions represent parts of a whole divided into three equal parts.
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Proper fractions are when the numberator is less than or equal to the denominator. So, the only three fractions that can be proper with the denominator as three are: 1/3, which equals approx. 0.333333333 2/3, which equals approx. 0.666666667 3/3, which equals 1.
To put fractions into opposite fractions, all you have to do is flip it so that the numerator becomes the denominator and the denominator becomes the numerator. This is called a reciprocal. Example: The opposite of 3/5 is 5/3
For a _positive_ fraction to be proper and in lowest terms, the numerator must be less than the denominator and be relatively prime. For denominator 1: 0 possible numerators. For denominator 2: 1 possible numerator. For denominator 3: 2 possible numerators. For denominator 4: 2 possible numerators. For denominator 5: 4 possible numerators. For denominator 6: 2 possible numerators. For denominator 7: 6 possible numerators. For denominator 8: 4 possible numerators. For denominator 9: 6 possible numerators. Adding all of them together gives 27 positive proper fractions in lowest terms. Symmetrically, there are 27 negative proper fractions in lowest terms. Also, 0/1 is in lowest terms by the above definition. So in total, there are 55 proper fractions in lowest terms with denominator being an integer from 1 to 9.
If two fractions have a common denominator of 8, it means that both fractions have 8 as their denominator. The fractions could be any two numbers as their numerators, such as 3/8 and 5/8, or 1/8 and 7/8. As long as the denominator is 8 for both fractions, the numerators can vary.
When two or more fractions have the same denominator, it means they have a common base for their fractional parts. This allows for easier comparison and addition or subtraction of the fractions, as the denominators are already aligned. By having the same denominator, the fractions can be easily manipulated by adding or subtracting the numerators while keeping the denominator constant. This simplifies operations involving fractions with common denominators.
At least two fractions are needed to determine a common denominator.