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- The additive inverse property is essential in applying the Division and Multiplication Properties of Equality when solving equations. When solving an equation like $3x + 2 = 11$, we can isolate the variable $x$ by subtracting $2$ from both sides, using the additive inverse property: $3x + 2 - 2 = 11 - 2$, which simplifies to $3x = 9$.
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An additive inverse of a number is defined as the value, which on adding with the original number results in zero value. It is the value we add to a number to yield zero. Suppose, a is the original number, then its additive inverse will be minus of a i.e.,-a, such that; a+ (-a) = a – a = 0. Example:
Additive inverse of a number is a number that, when added to the original number, gives the sum of 0. In simple words, the sum of a number and its additive inverse is always 0. Mathematically, the additive inverse of a real number n is denoted as – n. Similarly, the additive inverse of – n is n.
- The additive inverse of 0 is 0 itself.
- Except for 0, the additive inverse of all other whole numbers (natural numbers) is always negative, since all the natural numbers are positive.
- The sum of a number and its additive identity is the number itself, whereas the sum of a number and its additive inverse is 0.
In a field, every element must have an additive inverse that ensures closure under addition and satisfies properties like associativity and commutativity. This requirement enables mathematicians to perform more complex operations and proofs efficiently.
The additive inverse property is crucial in the context of adding and subtracting integers, as well as solving equations using the Division and Multiplication Properties of Equality. Recognizing and applying the additive inverse property is essential for manipulating and simplifying algebraic expressions involving signed numbers. Review Questions.
The additive inverse of a number is its opposite number. If a number is added to its additive inverse, the sum of both the numbers becomes zero. The simple rule is to change the positive number to a negative number and vice versa. We know that, 7+ (-7) =0.
May 28, 2023 · Definition: Inverse Properties. Inverse Property of Addition for any real number a, \ [a + (−a) = 0\] −a is the additive inverse of a. Inverse Property of Multiplication for any real number a ≠ 0, \ [a \cdot \dfrac {1} {a} = 1\] \ (\dfrac {1} {a}\) is the multiplicative inverse of a.
Properties of Inverse Operations. Inverse Additive Property; The value, which, when added to the original number gives 0, is known as the additive inverse. Suppose, x is the original number, then its additive inverse will be minus of x, i.e., $-$$\text{x}$, such that: $\text{x + ( – x ) = x – x} = 0$ For example, $6+( $ $-$ $ 6)=0$.
