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Let a and b be rational numbers is a•b rational or irrational

2 Answers

7 votes

Answer:

it is rational

Explanation:

Let a and b be rational numbers is a•b rational or irrational-example-1
User Kmera
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3 votes

Answer:

it is irrational

Explanation:

A rational number is one that can be written as n/m, where n and m are both integers.

Let a be a rational number such that a=n/m

Let b be a rational number such that b=p/q.

Notice n,m, p, and q are all integers.

When we divide a by b, a/b=(n/m)/(p/q)

But we know that complex fractions can be simplified by multiplying the numerator by the denominator.

a/b=(n/m)*(q/p)=nq/mp.

One of the properties of integers is closure under multiplication: that is to say, the product of integers is always an integer. So nq and mp are both integers.

By the definition of rational numbers nq/mp is a rational number. Therefore, a/b is a rational number.

User Takuhii
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