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A fraction multiplied by its reciprocal is always equal to one. This is because the reciprocal is an inversion of the fraction. The denominator of a fraction is the same number as the numerator of the reciprocal, and vice versa. The product of this is a fraction with the same numbers for the denominator and reciprocal, which is also known as an equivalent fraction. Equivalent fractions are always equal to one.

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Q: What is the product of two numbers that are reciprocals of one another explain why this is always the case?
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Related questions

What are the two conditional statements from the following Two numbers are reciprocals if and only if their product is 1?

If two numbers are reciprocals, then their product is 1. If the product of two numbers is 1, then they are reciprocals.


What do you call two numbers and their product is one?

The numbers are reciprocals of one another.


What is the product of two numbers that are reciprocals of one another?

1


What is the product of two numbers that are opposite reciprocals?

I have a feeling that you wrote "opposite reciprocals"where you only needed to write "reciprocals".Their product is ' 1 '.


Two numbers are if their product is -1?

Two numbers are negative reciprocals if their product is -1. The numbers 1/2 and -2 are negative reciprocals. Their product is -1. This is often seen in problems involving the slopes of two lines. The slopes of perpendicular lines are negative reciprocals. Their product is -1.


How can you tell if two numbers are reciprocals?

If you multiply two reciprocals, their product must be 1.


What are two numbers with a product of one?

They're known as reciprocals.


What are two numbers whose product is one called?

Reciprocals, or multiplicative inverses


What is it called when two numbers have a product that is one?

The Two numbers are reciprocals of each number


What is two numbers whose product is one?

They're known as reciprocals.


What two numbers whose product is one?

They're known as reciprocals.


What Two numbers with a product of 1 are called?

reciprocals, multiplicative inverses


What are two numbers that are blank if their product is negative 1?

The numbers are negative reciprocals of each other.


The sum of two numbers is 10 their product is 20 the sum of reciprocals is what?

It is 0.5


One of the two numbers whose product is 1?

Any two numbers whose product is '1' are each others' reciprocals.


What do pairs of numbers whose product is 1 called?

They are called multiplicative inverses or reciprocals of each other.


What are two numbers whose product equals one called?

reciprocals or multiplicative inverses


Two numbers with a product of one?

2 and 0.5 They're known as reciprocals.


Is the sum of the reciprocals 1?

No, the product of reciprocals is 1.


Find the sum of the reciprocals of two real numbers given that these numbers have a sum of 150 and a product of 40?

1/x + 1/y = (y+x)/xy But y + x = sum = 150, and xy = product = 40 So sum of reciprocals = 150/40 = 3.75


What are two numbers whose product is one?

2 x .5 = 1 They're known as reciprocals.


What are resiprocals?

For example, the reciprocal of 3 is 1/3. Two numbers are reciprocals (each is the reciprocal of the other) if their product is 1.


If the sum of two numbers is 7 and there product is 25 what is the sum of there reciprocals?

Suppose the two numbers are x and y. Then, the sum of THEIR reciprocals is 1/x + 1/y = y/xy + x/xy = (y + x)/xy = 7/25


Is the reciprical of a product the product of the two reciprocals?

Yes.


What are two irrational numbers whose product is rational?

Make the two irrational numbers reciprocals of each other. Ex.) 1/pi x pi = 1