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Those letters are indeed often used to represent integers. But in practice, it's best to always check what assumptions are made. If certain variables (letters) are meant to be integers only, for example for some theorem, this should be stated explicitly.
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Can the product of two rational numbers be irrational?
No.Suppose a and b are two rational numbers.Then they can be written as follows: a = p/q, b = r/s where p, q, r and s are integers and q, s >0.Then a*b = (p*r)/(q*s).Using the properties of integers, p*r and q*s are integers and q*s is non-zero. So a*b can be expressed as a ratio of two integers and so the product is rational.
Express the folling in the form p q where pand q are integers and q is not equal to 0?
0.142678
When can you say that the given number is a rational?
A number is said to be rational if it can be expressed as a ratio of two integers. That is, a number x is rational if and only if it is equivalent to p/q for some integers p and q where q is not 0.
How do you express the Ratio of two integers?
The ratio of two integers P and Q can be expressed as P : Q or P/Q. In both cases, you may divided P and Q by their greatest common factor so as to express the ratio in its simplest form. Alternatively, you may multiply both by some number so that the first part is 1 or the second part is 1 (both unit ratios), or the second part is 100 (a percentage), or a million (part per million) and so on.
Is three elevenths a rational or irrational number and why?
Rational.In mathematics, a rational number is any numberthat can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q.
What is the difference between irrational numbers and integers?
An irrational number cannot be expressed as a ratio in the form p/q where p and q are integers and q > 0. Integers can be.
How do you express a numbers a ratio of two integers?
The ratio of two integers, p and q where q is not 0, can be expressed as p:q or p/q.
Why are integers always included in rational numbers?
A rational number is a number than can be written p/q with p and q integers Any integers can be written this was with q=1
What are rational numbers but not integers?
The vast majority of rational numbers are not integers. They are numbers which can be written in the form p/q where p and q are integers which are co-prime and q > 1.
What are rational numbers that are also integers?
All integers {..., -2, -1, 0, 1, 2, ...} are rational numbers because they can be expressed as p/q where p and q are integers. Let p equal whatever the integer is and q equal 1. Then p/q = p/1 = p where p is any integer. Thus, all integers are rational numbers.
How does every rational number have an additive inverse?
By definition, every rational number x can be expressed as a ratio p/q where p and q are integers and q is not zero. Consider -p/q. Then by the properties of integers, -p is an integer and is the additive inverse of p. Therefore p + (-p) = 0Then p/q + (-p/q) = [p + (-p)] /q = 0/q.Also, -p/q is a ratio of two integers, with q non-zero and so -p/q is also a rational number. That is, -p/q is the additive inverse of x, expressed as a ratio.
Prove that if a and b are rational numbers then a multiplied by b is a rational number?
If a is rational then there exist integers p and q such that a = p/q where q>0. Similarly, b = r/s for some integers r and s (s>0) Then a*b = p/q * r/s = (p*r)/(q*s) Now, since p, q r and s are integers, p*r and q*s are integers. Also, q and s > 0 means that q*s > 0 Thus a*b can be expressed as x/y where p and r are integers implies that x = p*r is an integer q and s are positive integers implies that y = q*s is a positive integer. That is, a*b is rational.
What is standard form of rational numbers?
The standard form is p/q where p and q are integers and q > 0.
What is the proper fraction?
A proper fraction is a ratio in the form p/q where p and q are integers and q>0.
What is negative rational numbers?
They are numbers that can be expressed as -p/q where p and q are positive integers.
What tule of number cannot be written as a fraction p\q where p and q are integers and q is not equal to zero?
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Can the product of two rational numbers be irrational?
No.Suppose a and b are two rational numbers.Then they can be written as follows: a = p/q, b = r/s where p, q, r and s are integers and q, s >0.Then a*b = (p*r)/(q*s).Using the properties of integers, p*r and q*s are integers and q*s is non-zero. So a*b can be expressed as a ratio of two integers and so the product is rational.
