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# Why is the reciprocal of the opposite of a nonzero number the opposite of the reciprocal of the number?

Updated: 4/28/2022

Wiki User

11y ago

Taking the reciprocal (multiplicative inverse) does not affect the positive or negative status of an integer. So the reciprocal of a negative number is negative and the reciprocal of a positive number is positive. The reciprocals will be opposites (positive/negative) just as the original numbers were.

Wiki User

11y ago

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Q: Why is the reciprocal of the opposite of a nonzero number the opposite of the reciprocal of the number?
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### Why is the reciprocal of a nonzero number is not the same as the opposite of the number?

Because "opposite" doesn't mean anything with respect to numbers, or rather, it doesn't have a unique and definite meaning with respect to numbers.

### Dividing by a nonzero number is the same as multiplying by the?

What is the inverse reciprocal of 0.01

### What is the product of any nonzero real number and its reciprocal?

The product of any nonzero real number and its reciprocal is the number 1. This can be mathematically given as n multiplied by 1/n, where n represents the nonzero real number. The product of these two terms is 1.

### Is the product of a nonzero number and its reciprocal is 0?

Let's say that the nonzero real number is n. Then the reciprocal would be (1/n). So the product is the following n*(1/n)=(n/n)=1 In conclusion the product of any nonzero real number and it's reciprocal is always 1.

### What are the differences between the opposite of a non-zero number and the reciprocal of that number?

The answer depends on what you mean by the "opposite" of a number. A reciprocal is one type of opposite: it is the multiplicative opposite.

### How are the reciprocal of a nonzero number and the multiplicative inverse of the number related?

1/7=7 Superscript -1

### What are similarities and differences between the opposite of a non-zero number and the reciprocal of that number?

The answer depends on what you mean by the "opposite" of a number. A reciprocal is one type of opposite: it is the multiplicative opposite.

### What is the name of the product of a nonzero number and its reciprocal is 1?

Yes, it is."The name of the product of a non-zero number and its reciprocal is 1" is TAUTOLOGY.

### What is the opposite of a nonzero rational number?

The answer depends on whether you mean an additive opposite or a multiplicative opposite.

### How are the reciprocal of nonzero number and the multiplicative inverse of the numbers related?

For numbers with ordinary multiplication defined on them, they are the same.

### What is the product of a number and a recipical?

The product of a number and its reciprocal is one. A reciprocal is, quite simply, the opposite of the number.