You still additive inverse to find -12 2/3 - -8 5/6
To find the additive inverse, we can simply change the sign of the given number.
The additive inverse of -12 2/3 is 12 2/3, and the additive inverse of -(-8 5/6) is 8 5/6.
So, -12 2/3 - -8 5/6 is equal to 12 2/3 + 8 5/6.
To find the sum of -12 2/3 and -(-8 5/6), we can rewrite the problem as follows:
-12 2/3 - -8 5/6
Step 1: To simplify, we need to convert the mixed numbers into improper fractions.
-12 2/3 = -((3 * 12) + 2)/3 = -((36 + 2)/3) = -(38/3)
-8 5/6 = -((6 * 8) + 5)/6 = -((48 + 5)/6) = -(53/6)
Step 2: Now that we have -38/3 - (-53/6), we can simplify further by finding the additive inverse of the second fraction. The additive inverse of a fraction is the same fraction with its sign changed.
So, the additive inverse of -53/6 is 53/6.
Step 3: Now we can rewrite the problem using the additive inverse:
-38/3 + 53/6
Step 4: We need to find a common denominator. In this case, the lowest common denominator (LCD) is 6, so we need to convert -38/3 to have a denominator of 6.
-38/3 = -((3 * 38)/3) = -((114/3) = -38
Then the problem becomes:
-38/6 + 53/6
Step 5: Now we can simply add the fractions together because they have the same denominator:
-38/6 + 53/6 = (53 - 38)/6 = 15/6
Step 6: We can further simplify the fraction, if needed. In this case, 15/6 can simplify to 5/2.
Therefore, -12 2/3 - -8 5/6 is equal to 5/2.