Question

Solve both the parts in the given below options and check whether they are the same or not.
(a) \[\dfrac{6}{11}\times \dfrac{-2}{7}\]
(b) \[\dfrac{-2}{7}\times \dfrac{6}{11}\]

Answer 1

Hint: In this question, we first need to consider the first part and then multiply the numerators and denominators respectively. Now, consider the second part and then multiply numerators and denominators respectively. Then from the result using the commutative property of multiplication we can conclude whether they are the same or not.

Complete step-by-step answer:
Now, form the given question we have \[\dfrac{6}{11}\times \dfrac{-2}{7}\] and \[\dfrac{-2}{7}\times \dfrac{6}{11}\]
Let us now look at the multiplication property
Commutative Property: When two numbers are multiplied together, the product is the same regardless of the order of the multiplicands.
Example: \[4\times 2=2\times 4\]
Now, let us consider the first part in the given question
\[\Rightarrow \dfrac{6}{11}\times \dfrac{-2}{7}\]
Let us now multiply the respective numerators and denominators
\[\Rightarrow \dfrac{6\times \left( -2 \right)}{11\times 7}\]
Now, on further simplification we can write it as
\[\Rightarrow \dfrac{-12}{77}\]
Let us now consider the second part of the given question
\[\Rightarrow \dfrac{-2}{7}\times \dfrac{6}{11}\]
Now, on multiplying the respective numerators and denominators we get,
 \[\Rightarrow \dfrac{\left( -2 \right)\times 6}{7\times 11}\]
Now, on multiplying the respective terms and simplifying further we get,
\[\Rightarrow \dfrac{-12}{77}\]
Now, on comparing the values in both the parts and using the commutative property of multiplication we can conclude that they are the same.
Hence, \[\dfrac{6}{11}\times \dfrac{-2}{7}\] and \[\dfrac{-2}{7}\times \dfrac{6}{11}\] are same.

Note: Instead of multiplying the respective numerators and denominators we can also conclude using the commutative property of multiplication directly. Both the methods give the same result.
It is important to note that we need to multiply the numerators respectively and denominators respectively not one with the other. It is also to be noted that we should not interchange the numerator and denominator while noting.