Use additive inverse to find -12 2/3- (-8 ,5/6)
To find the sum of -12 2/3 and -8 5/6 using additive inverse, we first need to convert both numbers to their improper fraction form.
Converting -12 2/3 to an improper fraction:
-12 * 3 = -36
-36 + 2 = -34
-34/3
Converting -8 5/6 to an improper fraction:
-8 * 6 = -48
-48 + 5 = -43
-43/6
Now we can use additive inverse by changing the sign of the second fraction and adding both fractions:
-34/3 + (-(-43/6))
When we multiply the negative sign inside the parentheses, it changes the sign of the second fraction:
-34/3 + (43/6)
To add these fractions, we need a common denominator, which is 6:
-34/3 * 2/2 = -68/6
Now we can add the fractions:
-68/6 + 43/6 = -25/6
So, -12 2/3 - (-8 5/6) is equal to -25/6.
To find the sum of -12 2/3 and the additive inverse of (-8 5/6), follow these steps:
1. Find the additive inverse of (-8 5/6):
The additive inverse of a number is the number that, when added to the original number, gives a sum of zero.
To find the additive inverse, change the sign of the number. In this case, change the sign of -8 5/6 to positive.
-(-8 5/6) = 8 5/6
Therefore, the additive inverse of (-8 5/6) is 8 5/6.
2. Add -12 2/3 and 8 5/6:
-12 2/3 + 8 5/6
To add these fractions with different denominators, we need to find a common denominator.
The least common multiple (LCM) of 3 and 6 is 6.
-12 2/3 can be written as -38/3.
8 5/6 can be written as 53/6.
Now, the addition becomes:
-38/3 + 53/6
3. Rewrite the fractions with the common denominator:
-38/3 = -76/6
53/6 = 53/6
Now, the addition becomes:
-76/6 + 53/6
4. Add the fractions:
-76/6 + 53/6 = -23/6
5. Simplify the fraction if possible:
The fraction -23/6 cannot be simplified further.
Therefore, the sum of -12 2/3 and the additive inverse of (-8 5/6) is -23/6.