define additive and multiplicative inverse with examples.
Answers
A multiplicative inverse is a reciprocal. What is a reciprocal? A reciprocal is one of a pair of numbers that when multiplied with another number equals the number 1. For example, if we have the number 7, the multiplicative inverse, or reciprocal, would be 1/7 because when you multiply 7 and 1/7 together, you get 1!
Example 1:
What is the multiplicative inverse of 15? In other words, which number when multiplied with 15 would give us the number 1 as a result? Let's solve this in an algebraic way, with x being the unknown multiplicative inverse.
Additive identity of numbers, as the name suggests, is a property of numbers which is applied when carrying out addition operations. The property states that when a number is added to zero it will give the same number. “Zero” is called the identity element, (also known as additive identity) If we add any number with zero, the resulting number will be the same number. This is true for any real numbers, complex numbers and even for imaginary numbers.
Suppose, a is any real number, then
a + 0 = a = 0 + a
For example, 120 + 0 = 120 illustrates identity property of addition, where 0 is the additive identity.
5 * x = 1
x = 1/15
That's it! It was really that simple! The multiplicative inverse of a number is that number as the denominator and 1 as the numerator. When we multiply 15 and 1/15, we get 1.
Example 2:
What is the multiplicative inverse of 1/4? Now this example is a little different because we are beginning with a fraction. Let's again solve this algebraically, with x being the unknown multiplicative inverse of 1/4.
1/4 * x = 1
x = 1 / (1/4)
(1/1) / (1/4) = (1/1) * (4/1) = 4
Remember that when you divide fractions, you must flip the numerator and denominator of the second fraction and then multiply. We got 4 as the multiplicative inverse of 1/4. Makes sense, right?
So, the conclusion that we can draw from these two examples is that when you have a whole number, the multiplicative inverse of that number will be that number in fraction form with the whole number as the denominator and 1 as the numerator. When you have a fraction with 1 as the numerator, the multiplicative inverse of that fraction will simply be the denominator of the fraction.
In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x⁻¹, is a number which when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse of a fraction a/b is b/a. For the multiplicative inverse of a real number, divide 1 by the number.