MCQ
Which of the following statement is true?
- AThe difference of two rational numbers is always a rational number.
- BAddition of two rational numbers is associative.
- CAddition of two rational numbers is commutative.
- ✓All of the above.
✓
Answer
Correct option: D.
All of the above.
As we know that difference of two rational numbers is always a rational number.
$\Rightarrow\frac{4}{9}-\frac{2}{9}=\frac{2}{9}($The difference of two rational numbers is always a rational number$)$
And, $-\frac{3}{7}+\frac{1}{3}=\frac{1}{3}+\Big(-\frac{3}{7}\Big)$
$\Rightarrow-\frac{2}{21}=-\frac{2}{21} ($Addition of two rational numbers is commutative$)$
Also, $\frac{3}{15}\Big(\frac{4}{15}+\frac{2}{15}\Big)=\Big(\frac{3}{15}+\frac{2}{15}\Big)+\frac{2}{15}$
$\Rightarrow\frac{9}{15}=\frac{9}{15}($Addition of two numbers is associative$)$
There all the given statements are true.
$\Rightarrow\frac{4}{9}-\frac{2}{9}=\frac{2}{9}($The difference of two rational numbers is always a rational number$)$
And, $-\frac{3}{7}+\frac{1}{3}=\frac{1}{3}+\Big(-\frac{3}{7}\Big)$
$\Rightarrow-\frac{2}{21}=-\frac{2}{21} ($Addition of two rational numbers is commutative$)$
Also, $\frac{3}{15}\Big(\frac{4}{15}+\frac{2}{15}\Big)=\Big(\frac{3}{15}+\frac{2}{15}\Big)+\frac{2}{15}$
$\Rightarrow\frac{9}{15}=\frac{9}{15}($Addition of two numbers is associative$)$
There all the given statements are true.
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