Which property is being used in the following:

$\frac{2}{3} + \frac{4}{7} = \frac{4}{7} + \frac{2}{3}$

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Additive identity

Commutative property of addition

Commutative property of multiplication

Associative property of addition

answer is B.

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Detailed Solution

The left hand side :

\frac{2}{3} + \frac{4}{7}

\frac{2 \times 7 + 4 \times 3}{7 \times 3}

⇒

\frac{2}{3} + \frac{4}{7}

\frac{14 + 12}{21}

∴

\frac{2}{3} + \frac{4}{7}

\frac{26}{21}

Similarly, the right hand side:

\frac{4}{7} + \frac{2}{3}

\frac{4 \times 3 + 2 \times 7}{7 \times 3}

⇒

\frac{4}{7} + \frac{2}{3}

\frac{12 + 14}{21}

∴

\frac{4}{7} + \frac{2}{3}

\frac{26}{21}

We can see that the values on both sides of the expression are the same.
We define an additive identity as a number that, when added to another number, gives the sum as the number itself. This means that the number 0 is an additive identity. Because any number added to 0 gives the sum as the number itself.
The commutative property of addition states that the order of terms added does not affect the sum of the terms. Similarly, the commutative property of multiplication states that the order of the numbers being multiplied does not affect the product.
The associative property of addition says that if more than two terms need to be added and we group the terms to perform the addition, the sum of the terms will not change even if the groups of the terms change.
Since 0, the additive identity is not involved in the terms being added in a given expression, we can rule out the first possibility.
When calculating the value of the left and right sides of the given expression, we saw that the order of the terms was changed and the sum of the terms was the same. This means that the given expression is an example of the commutative property of addition.
Hence, the correct option is (2).

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