the product of two rational numbers can always be written as\nan irrational number.\na whole number.\nan…
the product of two rational numbers can always be written as\nan irrational number.\na whole number.\nan integer.\na fraction.
Answer
Answer:
D. a fraction.
Explanation:
Step1: Recall definition of rational numbers
A rational number is of the form $\frac{a}{b}$ where $a,b\in\mathbb{Z}$ and $b\neq0$.
Step2: Let two rational numbers
Let the two rational numbers be $\frac{m}{n}$ and $\frac{p}{q}$ where $m,n,p,q\in\mathbb{Z}$ and $n\neq0,q\neq0$.
Step3: Calculate the product
The product is $\frac{m}{n}\times\frac{p}{q}=\frac{mp}{nq}$. Since $mp,nq\in\mathbb{Z}$ and $nq\neq0$, the product is a fraction.
Step4: Analyze other options
- An irrational number cannot be written as a fraction. The product of rationals is not irrational.
- A whole - number is a non - negative integer. For example, $\frac{1}{2}\times\frac{1}{3}=\frac{1}{6}$ which is not a whole number.
- An integer is a whole number or its negative. $\frac{1}{2}\times\frac{1}{3}=\frac{1}{6}$ is not an integer.