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Because a is rational, there exist integers m and n such that a=m/n.
Because b is rational, there exist integers p and q such that b=p/q.
Consider a+b. a+b=(m/n)+(p/q)=(mq/nq)+(pn/mq)=(mq+pn)/(nq).
(mq+pn) is an integer because the product of two integers is an integer, and the sum of two integers is an integer. nq is an integer since the product of two integers is an integer. Because a+b equals the quotient of two integers, a+b is rational.
What else can I help you with?
If x is a rational number and y is a rational number than is x plus y rational?
If both numbers are rational then x plus y is a rational number
How can you prove that 3 plus 2x⁵ is an irrational number where x⁵ is irrational?
1) Adding an irrational number and a rational number will always give you an irrational number. 2) Multiplying an irrational number by a non-zero rational number will always give you an irrational number.
Is a rational number plus a rational number always a rational number?
Yes, it is.
Are integers rational numbers?
Integers are whole numbers. Rational numbers can be fractions / decimals. But it is NEVER a whole number E.G. of rational numbers : 3/4 or 1.5
Why an irrational number plus an irrational number equal a rational?
Well, darling, when you add two irrational numbers together, they can sometimes magically cancel each other out in such a way that the sum ends up being a rational number. It's like mixing oil and water and somehow getting a delicious vinaigrette. Math can be a wild ride, honey.
Is a rational number plus a rational number rational?
Yes. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.
If x is a rational number and y is a rational number than is x plus y rational?
If both numbers are rational then x plus y is a rational number
What is an irrational plus two rational numbers?
Since the sum of two rational numbers is rational, the answer will be the same as for the sum of an irrational and a single rational number. It is always irrational.
Why does a rational number plus a rational number or a rational number multiplied by a rational number equal to rational number?
The way in which the binary functions, addition and multiplication, are defined on the set of rational numbers ensures that the set is closed under these two operations.
Are all mixed numbers rational?
Yes.A mixed number is a whole number plus a fraction.Fractions are rational, that is of the form c/dWhole numbers are rational - put them over 1 to form a[n improper] fraction a/b, eg 5 = 5/1The sum of two rational numbers is rational.
Why is the sum of an rational number and irrational number an irrational number?
The rational numbers form a field. In particular, the sum or difference of two rational numbers is rational. (This is easy to check directly). Suppose now that a + b = c, with a rational and c rational. Since b = c - a, it would have to be rational too. Thus you can't ever have a rational plus an irrational equalling a rational.
How can you prove that 3 plus 2x⁵ is an irrational number where x⁵ is irrational?
1) Adding an irrational number and a rational number will always give you an irrational number. 2) Multiplying an irrational number by a non-zero rational number will always give you an irrational number.
Is a rational number plus a rational number always a rational number?
Yes, it is.
Is a Rational number plus rational number equals rational number?
Yes, the sum is always rational.
Are integers rational numbers?
Integers are whole numbers. Rational numbers can be fractions / decimals. But it is NEVER a whole number E.G. of rational numbers : 3/4 or 1.5
Can a rational number plus an irrational number equal a rational number?
No, never.
Why is negative three a rational number?
Negative three is rational because it is a integer and if its a integer it is a rational. Integers are basically natural numbers plus the negtives and zero.
