Explain how the difference of a fraction or a rational number and its additive inverse is equal to zero.
not true.
The sum of a number and its additive inverse is Zero.
That is the definition of additive inverse.
To understand how the difference of a fraction or a rational number and its additive inverse is equal to zero, let's break it down step by step.
First, let's define a fraction or a rational number. A fraction is a number that represents a part of a whole, and it's written as a ratio of two integers, with a numerator and a denominator. For example, 1/2, 3/4, or 5/8 are all fractions.
Next, let's define the additive inverse of a number. The additive inverse of any number is the number that, when added to the original number, gives us zero. For example, the additive inverse of 5 is -5, because 5 + (-5) equals zero.
Now, let's consider a fraction, say, a/b. The additive inverse of this fraction would be -(a/b). To find the difference between these two fractions, we subtract the additive inverse from the original fraction:
a/b - (-a/b)
To subtract fractions, we need to find a common denominator. In this case, the common denominator is b, as it is already the denominator for both fractions. So we can rewrite the expression as:
(a - (-a))/(b)
When we subtract -a from a, we get a + a, which is 2a. So now our expression becomes:
2a/b
Here comes the key step. If we examine 2a/b, we notice that the numerator, 2a, is twice the value of a. However, the denominator, b, remains unchanged. This means that the value of 2a is twice the value of a divided by b, which is the same as the original fraction a/b.
In other words, 2a/b is equivalent to a/b. Therefore, the difference between a/b and its additive inverse, -(a/b), is zero:
a/b - (-a/b) = a/b + a/b = 2a/b = a/b
So, the difference of a fraction or a rational number and its additive inverse is always equal to zero.