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Yes. The simple answer is that rational fractions are infinitely dense. A longer proof follows:
Suppose you have two fractions a/b and c/d where a, b, c and d are integers and b, d are positive integers.
Without loss of generality, assume a/b < c/d.
The inequality implies that ad < bc so that bc-ad>0 . . . . . . . . . . . . . . . . . . . (I)
Consider (ad + bc)/(2bd)
Then (ad+bc)/2bd - a/b = (ad+bc)/2bd - 2ad/2bd = (bc-ad)/2bd
By definition, b and d are positive so bd is positive and by result (I), the numerator is positive.
That is to say, (ad+bc)/2bd - a/b > 0 or (ad+bc)/2bd > a/b.
Similarly, by considering c/d - (ad+bc)/2bd is can be shown that c/d > (ad+bc)/2bd.
Combining these results,
a/b < (ad+bc)/2bd < c/d.
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Can you always find another fraction in between two fractions and why?
Yes. The set of rational numbers is infinitely dense.If p/q and r/s are any two fractions then (p/q + r/s)/2 is a fraction which is between the two.
What it the greatest possible fraction greater than zero?
There is no such fraction. Fractions are infinitely dense and, between any two fractions, there are infinitely many more fractions. It is, therefore, always possible to find a larger proper fraction.For example,9/10 < 99/100 < 999/1000 < 9999/10000 and so on, for ever and ever.There is no greatest fraction.
How do you simplify when its just one number in fractions?
A fraction always has one number on top (the numerator), and another number on the bottom (the denominator). If it doesn't have both of those, then it's not a fraction.
What fractions is nearest to 2?
There can be no such thing as a nearest fraction since, given any fraction, it is always possible to find a fraction that is nearer.
Do you divide equivalent fractions?
Any fraction divided by an equivalent fraction will always equal one.Any fraction divided by an equivalent fraction will always equal one.Any fraction divided by an equivalent fraction will always equal one.Any fraction divided by an equivalent fraction will always equal one.
Can you always find another fraction in between two fractions and why?
Yes. The set of rational numbers is infinitely dense.If p/q and r/s are any two fractions then (p/q + r/s)/2 is a fraction which is between the two.
How many fractions are between three-fourths and one-half?
Whatever two fractions you name, no matter how close together they are, I can always name another fraction between them. In fact, there are an infinite number of fractions between any two fractions, no matter how close together they are. That goes for three-fourths and one-half.
When dividing fractions does the answer always end with an improper fraction?
Not always. There are times when division of fractions results in a non-improper fraction.
What comes after 2 3 in fractions?
Well, darling, after 2/3 comes 3/3, which is the same as 1 whole. So, if you're counting in fractions, it goes 1/3, 2/3, 3/3, and then you're back to square one with a full pie. Hope that clears things up for you!
What it the greatest possible fraction greater than zero?
There is no such fraction. Fractions are infinitely dense and, between any two fractions, there are infinitely many more fractions. It is, therefore, always possible to find a larger proper fraction.For example,9/10 < 99/100 < 999/1000 < 9999/10000 and so on, for ever and ever.There is no greatest fraction.
How do you simplify when its just one number in fractions?
A fraction always has one number on top (the numerator), and another number on the bottom (the denominator). If it doesn't have both of those, then it's not a fraction.
What is the smallest of all the fractions?
There is no complete answer because a fraction can always be reduced sot there is no smallest fraction.
What fractions is nearest to 2?
There can be no such thing as a nearest fraction since, given any fraction, it is always possible to find a fraction that is nearer.
Do you divide equivalent fractions?
Any fraction divided by an equivalent fraction will always equal one.Any fraction divided by an equivalent fraction will always equal one.Any fraction divided by an equivalent fraction will always equal one.Any fraction divided by an equivalent fraction will always equal one.
What is the product of two numbers that are reciprocals of one another explain why this is always the case?
A fraction multiplied by its reciprocal is always equal to one. This is because the reciprocal is an inversion of the fraction. The denominator of a fraction is the same number as the numerator of the reciprocal, and vice versa. The product of this is a fraction with the same numbers for the denominator and reciprocal, which is also known as an equivalent fraction. Equivalent fractions are always equal to one.
Are rational number is a fraction sometimes always or never?
Rational numbers can always be expressed as fractions.
Can fractions always be written as decimals?
You can always convert a fraction to a decimal. For some fractions, you'll get terminating decimals. For example, 1/8 = 0.125. For other fractions, you get repeating decimals, such as 1/7 = 0.142857 142857 142857...To convert the fraction to a decimal, just divide the numerator by the denominator, for example on a calculator.
