What is a reciprocal and when is it used to divide?
A fraction turned upside down
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A reciprocal is the multiplicative inverse of a number. In simple terms, it is a number that when multiplied by the original number gives a product of 1. Mathematically, the reciprocal of a number 'a' is denoted as 1/a.
Reciprocals are most commonly used in division. Instead of directly dividing one number by another, we can multiply the first number by the reciprocal of the second number. This is called "multiplication by the reciprocal" or "multiplying by the inverse."
For example, let's say we want to divide 8 by 2. Instead of performing the division operation, we can multiply 8 by the reciprocal of 2, which is 1/2. So, 8 divided by 2 can be expressed as 8 multiplied by the reciprocal of 2, which is 8 * (1/2) = 4.
Using reciprocals to divide can also be helpful when dealing with fractions. For instance, if we want to divide 3/4 by 5/6, we can multiply 3/4 by the reciprocal of 5/6, which is 6/5. So, (3/4) divided by (5/6) can be rewritten as (3/4) multiplied by (6/5), resulting in (3/4) * (6/5) = 18/20.
In summary, the reciprocal is the multiplicative inverse of a number, and it is used to divide by multiplying the number by its reciprocal instead of performing the division operation directly.