Question

Which property is illustrated by the following statement?
$(16 + 18) + 20 = (18 + 16) + 20$

Answer 1

Hint:
Observe the two sides of the equation. Find the difference. We can see the only difference is $16 + 18$ and $18 + 16$. Thus we can identify that the commutative property is used here. Explain the commutative property of addition in general.

Complete step by step solution:
Given that $(16 + 18) + 20 = (18 + 16) + 20$
The only difference we can see on both sides of the equation is the order of the numbers, $16$ and $18$.
Subtracting $20$ from both sides we get,
$16 + 18 = 18 + 16$
This addition of two numbers does not depend on the order in which they are written.
This property is called Commutativity.
Commutative property of addition states that changing the order of addends does not change the sum.
In general we can say that, for any two numbers $a$ and $b$, $a + b = b + a$.
This property can be extended to any number of terms apart from binary addition.

Therefore the answer is Commutative property.

Additional information:
Commutative property is also applicable in case of multiplication. We know that for any two numbers $a$ and $b$, $a \times b = b \times a$.
But it does not hold in case of subtraction and division.
We have $a - b \ne b - a$ and $\dfrac{a}{b} \ne \dfrac{b}{a}$ in most cases.
But there are exceptional cases as well. If $a$ and $b$ are equal, then $a - b = b - a = 0$ and $\dfrac{a}{b} = \dfrac{b}{a} = 1$.
Commutative property, associative property and distributive property are the three fundamental properties defined for any binary operation.

Note:
Don’t confuse commutative property with associative property. Associative property is used when there are three numbers and the operations are the same. It states that $a \times (b \times c) = (a \times b) \times c$, for some operation $ \times $.