0
How many positive fractions in simplest form have denominators of 100 where the numerator does not share a common factor other than 1 with the denominator 100?
Wiki User
∙ 10y ago
There are 40.
The question is asking how how many numbers 1-99 are relatively prime to 100.
The prime factorisation of 100 is 22 x 52, so all numbers 1-99 which do not have either of 2 and 5 in their prime factorization will have no common factor with 100 other than 1. ie the numbers which are some of the primes 3, 7, 11, 13, ... multiplied together, along with the unit fraction (1/100).
Thus there are:
- The 1 unit fraction
- The 23 primes {3, 7, ..., 97};
- The 9 composites of 3 with another one of the primes {3, 7, ..., 31};
- The 3 composites of 32 with another one of the primes {3, 7, 11};
- The 1 composite of 34;
- The 3 composites of 7 with one other prime factor {7, 11, 13}.
Making 1 + 23 + 9 + 3 + 1 + 3 = 40 positive fractions in simplest form with a denominator of 100 and no common factor other than 1.
Wiki User
∙ 10y ago
Add your answer:
Earn +20 pts
Why is the recipical of A fraction less than one is always a fraction greater than one?
Fractions that are less than one are known as proper fractions. Their denominators are greater than their numerators. Their reciprocals would have numerators greater than their denominators, making them improper. Improper fractions are greater than one.
When numerator the same list fractions from list to greatest?
If the numerator is the same, the fraction with the largest denominator has the lowest value (assuming all fractions are positive numbers).
Are all fractions that have a numerator of 1 in simplest form?
Basically yes. If you want to be pedantic about it, though, there is the exception when the denominator is negative. Convention requires the simplest form to have a negative numerator (-1) and a positive denominator.
How do you you reduce a fraction with a negative number as a numerator?
To reduce a fraction with a negative number as a numerator, you can first simplify the fraction by finding the greatest common divisor (GCD) of the numerator and denominator. Then, divide both the numerator and denominator by their GCD and the negative sign remains unchanged. This will result in a reduced fraction with a negative numerator.
Are all fractions that have a numerator of 1 in simplest form explain?
Yes, that is true. With all positive fractions that can be reduced, the numerator becomes a smaller positive whole number. There is no smaller positive whole number than one, therefore all fractions that have a numerator of 1 are in their simplest form. You can tell if a fraction is in its simplest form by finding the the GCF of the nmerator and the denominator. If the GCF is 1, the fraction is in its simplest form. The GCF of any number and 1 is 1, therefore all fractions that have a numerator of 1 are in their simplest form.
Why is the recipical of A fraction less than one is always a fraction greater than one?
Fractions that are less than one are known as proper fractions. Their denominators are greater than their numerators. Their reciprocals would have numerators greater than their denominators, making them improper. Improper fractions are greater than one.
When numerator the same list fractions from list to greatest?
If the numerator is the same, the fraction with the largest denominator has the lowest value (assuming all fractions are positive numbers).
How do you know if a fraction is smaller?
If one fraction is negative and one is positive, you automatically know that the negative fraction is smaller. If both fractions are positive and have the same denominator, the one with the smallest numerator is smaller. If both fractions are negative and have the same denominator, the one with the larger numerator is smaller. If fractions have different denominators, convert the fractions to the same denominator to find which one is smaller. For example: 2/5 and 1/3 2/5 = 6/15 1/3 = 5/15 1/3 is smaller than 2/5. If the above fractions were negative, -6/15 is less than -5/15.
What are fractions with the numerator 1 called?
A unit fraction is a rational number written as a fraction where the numerator is one and the denominator is a positive integer. A unit fraction is therefore the reciprocal of a positive integer, 1/n.
If 2 fractions have the same numerator but different denominator how can you tell which is greater?
In that case, and assuming both fractions are positive, the one with the larger denominator is the smaller fraction, because you are dividing by a larger number.
Are all fractions that have a numerator of 1 in simplest form?
Basically yes. If you want to be pedantic about it, though, there is the exception when the denominator is negative. Convention requires the simplest form to have a negative numerator (-1) and a positive denominator.
Is A Fraction Negative if it has a negative numerator?
If the numerator is negative and the denominator is positive then the fraction will be negative. If the numerator is negative and the denominator is negative too then the fraction will be positive.
How do you you reduce a fraction with a negative number as a numerator?
To reduce a fraction with a negative number as a numerator, you can first simplify the fraction by finding the greatest common divisor (GCD) of the numerator and denominator. Then, divide both the numerator and denominator by their GCD and the negative sign remains unchanged. This will result in a reduced fraction with a negative numerator.
Are all fractions that have a numerator of 1 in simplest form explain?
Yes, that is true. With all positive fractions that can be reduced, the numerator becomes a smaller positive whole number. There is no smaller positive whole number than one, therefore all fractions that have a numerator of 1 are in their simplest form. You can tell if a fraction is in its simplest form by finding the the GCF of the nmerator and the denominator. If the GCF is 1, the fraction is in its simplest form. The GCF of any number and 1 is 1, therefore all fractions that have a numerator of 1 are in their simplest form.
If you have a fraction and both the numerator and the denominator are negative and you simplify it would the numerator and denominator stay negative?
The simplification will be positive. In other words, the numerator and the denominator will NOT stay negative.
What is the meaning of the least common denominator?
Given a set of integers, their least common denominator is the smallest positive integer which is a multiple of each member of the set. The definition is extended to fractions where the LCD refers to the LCD of their denominators.
What happens when decrease in numerator and increase in denominator?
The fraction gets smaller or increases, depending on whether the numerator and denominator are positive or negative.
