Opposite
In mathematics, the term “opposite” is often used in geometric and algebraic contexts
In mathematics, the term “opposite” is often used in geometric and algebraic contexts.
In geometry, the term “opposite” is commonly used when referring to sides, angles, or vertices of a shape or figure. For example, in a triangle, the side opposite to a particular angle is the one that does not directly connect to that angle. Similarly, the vertex opposite to a particular side is the one that is not directly connected to that side.
In algebra, the term “opposite” is used to describe numbers that have the same magnitude but different signs. For example, the number 5 and -5 are opposites since they are the same distance from zero on the number line but in opposite directions. In general, the opposite of a positive number is a negative number with the same magnitude, and the opposite of a negative number is a positive number with the same magnitude.
To find the opposite of a positive number, simply change its sign to negative. For example, the opposite of 3 is -3. Conversely, to find the opposite of a negative number, change its sign to positive. For example, the opposite of -7 is 7.
The concept of opposites plays an important role in algebraic operations such as addition and subtraction. When you add a number and its opposite, the result is always zero. For example, if you add 3 and -3, you get 0: 3 + (-3) = 0. Similarly, if you subtract a number from itself, the result is always zero. For example, if you subtract 5 from 5, you get 0: 5 – 5 = 0.
Understanding the concept of opposites is crucial in various mathematical applications, including solving equations, simplifying expressions, and understanding the relationships between positive and negative numbers.
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