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That is simply not true. For example, consider the quotient of 2/9 and 2/3.(2/9) / (2/3) = (2*3)/(9*2) = 3/9 = 1/3 which, unless I am very much mistaken, is not greater than one of the fractions: namely 2/3.

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Q: Why is the quotient of of two fractions always greater than either fractions?
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The sum of two whole numbers is always greater than either addend?

the sum of two whole numbers is always greater than either addend* * * * *No.Consider:5 is a whole number-3 is a whole number.Their sum is 2, which is notgreater than one of the addends (5).


Why is the product of two proper fractions less than either of the fractions?

A proper fraction is less than 1. Whenever you multiply something by a number < 1, the result (product) is less than the original number. So when you multiply a proper fraction by a number less one (such as another proper fraction, the product is less than the original proper fraction. The only time a product involving a given number is larger than the given number is when you multiply the given number by a number that is > 1. Since all proper fractions are < 1, products involving them are always less than the original given number.


What number is both rational and irrational?

None. A rational number is a number that can be written as the quotient of two integers where the divisor is not zero. An irrational number is a real number that cannot be written as the quotient of two integers where the divisor is not zero. Any given real number either can or cannot be written as the quotient of two integers. If it can, it is rational. If it cannot, it is irrational. You can't be both at the same time. The square root of -1 is not a real number and it cannot be written as the quotient of two integers, so it is neither rational nor irrational.


Can a real number be both rational and irrational?

No it cannot. Math is an exact science. As it has been said before, A number can either be written as the quotient of two integers or it cannot. You can't have it both ways.


What is the quotient of 4 and a number x increased by 6?

The expression for the quotient of 4 and a number x increased by 6 is (4/x) + 6. To simplify this expression, you would first divide 4 by x to get 4/x, then add 6 to the result. The final expression represents the quotient of 4 and x with an additional 6 added to it.