$-$ is a mathematical symbol that represents subtraction, which is the operation of removing or taking away a quantity from another quantity. It is a fundamental operation in algebra and is used to find the difference between two numbers or expressions.
congrats on reading the definition of $-$. now let's actually learn it.
The $-$ symbol is used to indicate subtraction in algebraic expressions and equations.
Subtraction is the inverse operation of addition, and the $-$ symbol can be used to undo the effect of addition.
Negative numbers are represented using the $-$ symbol, and they are used to represent quantities less than zero.
The $-$ symbol is also used to represent the additive inverse of a number, which is the number that, when added to the original number, results in a sum of zero.
In the context of algebra, the $-$ symbol is used to represent the subtraction of variables, constants, and expressions.
Review Questions
Explain how the $-$ symbol is used in algebraic expressions and equations.
In the context of algebra, the $-$ symbol is used to represent the subtraction of variables, constants, and expressions. It is used to find the difference between two quantities, such as $x - 3$ or $2a - 4b$. The $-$ symbol can also be used to represent the additive inverse of a number, which is the number that, when added to the original number, results in a sum of zero. For example, the additive inverse of $5$ is $-5$, and the additive inverse of $x$ is $-x$.
Describe the relationship between subtraction and addition in the context of algebra.
Subtraction is the inverse operation of addition in algebra. This means that the $-$ symbol can be used to undo the effect of addition. For example, if we have the expression $x + 5$, we can use the $-$ symbol to find the value of $x$ by subtracting $5$ from both sides of the equation: $x + 5 - 5 = 0$, which simplifies to $x = -5$. The $-$ symbol allows us to isolate variables and find unknown values in algebraic equations.
Analyze the role of negative numbers and the $-$ symbol in algebraic expressions and equations.
Negative numbers, represented by the $-$ symbol, play a crucial role in algebra. Negative numbers are used to represent quantities that are less than zero, such as $-3$ or $-x$. The $-$ symbol is used to indicate the subtraction of these negative numbers, which can lead to interesting and complex algebraic expressions and equations. For example, the expression $5 - (-3)$ can be simplified to $5 + 3 = 8$, demonstrating how the $-$ symbol is used to undo the effect of a negative number. Understanding the properties and operations of negative numbers, and how the $-$ symbol is used to represent them, is essential for success in algebraic problem-solving.