Answer:
2/3 and -3/2
Explanation:
Let's say that 2/3 is the regular fraction:
- It's reciprocal is 3/2 and its negative counterpart is -3/2.
Similarly, we could start with -3/2:
- It's reciprocal is -2/3 and the negative version of this (i.e., a negative * a negative) is 2/3.
Therefore, 2/3 and -3/2 are negative reciprocals of each other.
Finding a negative reciprocal algebraically:
Algebraically, you can determine a negative reciprocal of one fraction by multiplying -1 by the quotient of 1 and the fraction.
This is shown by the following formula:
m2 = -1/m1, where
- m1 is the slope of the line you're given,
- and m2 is the slope of the line you're trying to find.
Finding the negative reciprocal of 2/3 using the formula:
Since we're already given both slopes, let's pretend that we were only given 2/3 and wanted to find m2 (the negative reciprocal):
m2 = -1 / (2/3)
m2 = -1 * 3/2
m2 = -3/2
Finding the negative reciprocal of -3/2 using the formula:
Now let's pretend that we were only given -3/2 and wanted to find m2 (the negative reciprocal):
m2 = -1 / (-3/2)
m2 = -1 * -2/3
m2 = 2/3