# What Is An Opposite Reciprocal?

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## What Is An Opposite Reciprocal?

In mathematics, the opposite reciprocal is a term used to describe the relationship between two numbers. Specifically, the opposite reciprocal of a given number is the number that is it’s opposite (i.e., it has the opposite sign) and it’s reciprocal (i.e., it is the inverse of the original number).

To understand this concept better, let’s first review what it means to find the reciprocal of a number. The reciprocal of a number is simply its multiplicative inverse – in other words, the number that you would need to multiply by the original number to get a product of 1. For example, the reciprocal of 4 is 1/4, because 4 multiplied by 1/4 equals 1.

Now, to find the opposite reciprocal of a number, we need to first find its reciprocal, and then take the opposite (i.e., change its sign) of that reciprocal. For example, the opposite reciprocal of 2 is -1/2, because the reciprocal of 2 is 1/2, and the opposite of 1/2 is -1/2.

The opposite reciprocal is an important concept in mathematics because it can be used to find the slope of a line in a coordinate plane. Specifically, the slope of a line is equal to the opposite reciprocal of the line’s coefficient of x. For example, if the equation of a line is y = 3x + 2, then the slope of the line is -1/3, because the coefficient of x is 3, and the opposite reciprocal of 3 is -1/3.

In summary, the opposite reciprocal is a term used in mathematics to describe the relationship between two numbers. It is the number that is the opposite and reciprocal of a given number and is commonly used to find the slope of a line in a coordinate plane. By understanding this concept, students can build a stronger foundation for more advanced math concepts and problem-solving skills.

## FAQ

### What Is The Opposite Reciprocal Of 2?

The opposite reciprocal of 2 would be -1/2. To find the opposite reciprocal, first, find the reciprocal. The whole number 2 can be made into the fraction 2/1. After it is flipped over, it becomes its reciprocal, 1/2.

### What Is The Opposite Reciprocal Of One?

The multiplicative inverse of a number is a number that when multiplied with the original number produces 1. Therefore, the reciprocal of 1 is 1. Therefore, we get the final answer to the question as the opposite of 1 is -1 and the reciprocal of 1 is 1.

### What Is The Opposite Reciprocal Of 7?

If the given number is multiplied by its reciprocal, we get the value 1. Example: Reciprocal of the number 7 is 1/7. Thus, if we multiply 7 and 1/7, we get 1.

### What Is An Opposite Reciprocal In Geometry?

An opposite reciprocal is the fraction form of a number flipped upside down (that’s the reciprocal part), and with its sign changed (that’s the opposite part). Write those slopes side by side and it becomes more obvious: and are opposite reciprocals.

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