Question

................. are not associative for rational numbers.

• A. Addition and multiplication
• B. Subtraction and multiplication
• C. Subtraction and division
• D. Addition and division

Answer 1

Answer: (C)

Subtraction and division

Let us add three rational numbers $\frac{-7}{5},\frac{2}{-11}$ and $\frac{-13}{25}$

Then we know $\frac{-7}{5}+\left(\frac{2}{-11}+\frac{-13}{25}\right)=\left(\frac{-7}{5}+\frac{2}{-11}\right)+\frac{-13}{25}$

So we can say that addition is associative for rational numbers.

Now let us multiply three rational numbers $\frac{1}{6},6,\frac{4}{3}$

Then we get $\frac{1}{3}\times (6\times \frac{4}{3})=(\frac{1}{3}\times 6)\times \frac{4}{3}$

So we can say that multiplication is associative for rational numbers.

But when we divide three rational numbers in an order, the result so obtained will change if the order is changed.

For example: $(81÷9)÷3\ne$ $81÷(9÷3)$

And when we subtract three rational numbers, the result changes when we change the order of subtraction

For example: $5-(3-9)\ne (5-3)-2$

Therefore, subtraction and division are not associative for rational numbers.