What Is the Property of the Opposite of a Sum?
The property refers to how the opposite of a sum of real numbers is equal to the sum of the real numbers’ opposites. The property written out is -(a+b)=(-a)+(-b).
A simple example of this property in action could use the real numbers one and two, where a=1 and b=2. When a is added to b, the sum of the two numbers is three. The opposite of this sum is negative three.
Using the other side of the property,students can make a and b into their opposites, which would be negative one and negative two. When these two negative numbers are added together, the sum is negative three.
In both instances, the final result is negative three. This shows that the opposite of the sum of two real numbers will be the same as adding together the opposites of two real numbers.
Another quick example could be where a=7 and b=3. When a and b are added together, the sum is 10, and therefore, the opposite of this sum is negative 10. When the opposites of a and b, -7 and -3, are added together, the sum is negative 10 as well.
The property of the opposite of the sum is just one out of the five basic properties of addition, according to Hotmath.com. The other four properties are the identity property, the commutative property, the associative property and the property of opposites.