# Let a and b be rational numbers. Then by definitiona = m/n and b = p/p where m, n, p, and q are integersxy=m/n × p/qngso xy is the quotient of two integers.This proof shows that the product of two rational numbers is........a. an integerb. irrational c. rational d. a whole number

2 answers

###### Question:

Let a and b be rational numbers. Then by definition

a = m/n and b = p/p where m, n, p, and q are integers

xy=m/n × p/q

ng

so xy is the quotient of two integers.

This proof shows that the product of two rational numbers is........

a. an integer

b. irrational

c. rational

d. a whole number

a = m/n and b = p/p where m, n, p, and q are integers

xy=m/n × p/q

ng

so xy is the quotient of two integers.

This proof shows that the product of two rational numbers is........

a. an integer

b. irrational

c. rational

d. a whole number

## Answers

Answer:The product of two rational numbers is a rational numberStep-by-step explanation:I'll quickly recap the proof: a rational number is, by definition, the ratio between two integers. So, there exists four integers m,n,p,q such that[tex]a=\dfrac{m}{n},\quad b=\dfrac{p}{q}[/tex]If we multiply the fractions, we have[tex]ab = \dfrac{mp}{nq}[/tex]Now, mp and nq are multiplication of integers, and thus they are integers themselves. So, ab is also a ratio between integer, and thus rational.

Answer: the product of two rational numbers is a rational number!Step-by-step explanation:

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