Reciprocal of -8/-9

To find the reciprocal of a rational number, we need to invert or flip the given number. The reciprocal of a number is the number which, when multiplied by the given number, gives the result as 1.

Step 1: Convert the given fraction to its simplest form

To find the reciprocal of -8/-9, we first convert the fraction into its simplest form. We can simplify the given fraction by dividing both the numerator and denominator by their greatest common factor (GCF).

-8/-9 = 8/9

Step 2: Invert or flip the fraction

Once we have the simplified fraction, we need to invert or flip it to find its reciprocal.

Reciprocal of 8/9 = 9/8

Step 3: Check the reciprocal

To check whether the reciprocal is correct, we can multiply the given number with its reciprocal.

(8/9) x (9/8) = 1

Since the product of the given number and its reciprocal is 1, we can conclude that 9/8 is indeed the reciprocal of -8/-9.

Final Answer: The reciprocal of -8/-9 is 9/8.