Question

Which property is being used in the following
 $\dfrac{2}{3}+\dfrac{4}{7}=\dfrac{4}{7}+\dfrac{2}{3}$

(A). Additive identity of addition
(B). Commutative property of addition
(C). Commutative property of multiplication
(D). Associative property of addition

Answer 1

Hint: As we can see in the given question order of addition only changes and there is addition so only we will choose an option which has an additional word.
Also associative property of addition having three terms.

Complete step by step solution:
The given question is $\dfrac{2}{3}+\dfrac{4}{7}=\dfrac{4}{7}+\dfrac{2}{3}$
This is of the form $a+b=b+a$ ; which is a commutative property of addition because in addition if order changes the answer remains the same.
Here $\text{a=}\dfrac{2}{3}\text{ and }~\text{b=}\dfrac{4}{7}~$.
Additive identity states as follows, if a number is added the zero then gives the numbers itself
 i.e. $\text{a+0=a}$
Commutative property of multiplication
 $\Rightarrow \text{ a }\!\!\times\!\!\text{ b=b }\!\!\times\!\!\text{ a}$
Associative property of addition
 $\Rightarrow \text{ a+(b+c)=(a+b)+c}$
Hence answer is option B.

Note: As we can see there is a fraction in question and commutative property of addition is true for fraction as well because if we reverse order of addition the fraction answer remains the same.