Use the additive inverse to find -12 2/3 -(-8 5/6). Write the number as a mixed fraction
To find the sum of -12 2/3 and -(-8 5/6), we can use the additive inverse. The additive inverse of a number x is the number that, when added to x, will give a sum of zero.
First, let's change -12 2/3 and -(-8 5/6) to improper fractions:
-12 2/3 = -((3 * 12) + 2) / 3 = -38/3
-(-8 5/6) = -( -((6 * 8) + 5) / 6 ) = -53/6
Now, to find the sum, we can rewrite the equation as:
-38/3 + (-53/6)
To add these fractions, we need to find a common denominator. The least common multiple (LCM) of 3 and 6 is 6.
Next, we'll convert the fractions to have a common denominator of 6:
-38/3 = -((38 * 2) / (3 * 2)) = -76/6
-53/6 remains the same.
Now, we can add the fractions:
-76/6 + (-53/6) = -129/6
Finally, we can simplify the fraction -129/6 by dividing the numerator and denominator by their greatest common factor, which is 3:
(-129/3) / (6/3) = -43/2
Therefore, the sum of -12 2/3 and -(-8 5/6) is -43/2. In mixed fraction form, this is -21 1/2.
To find the additive inverse of a number, we simply change the sign of the number.
The additive inverse of -12 2/3 is 12 2/3.
Given the expression -12 2/3 -(-8 5/6), we can rewrite it as:
12 2/3 + 8 5/6.
Now, let's add the two mixed numbers.
First, we add the whole numbers: 12 + 8 = 20.
Next, we add the fractions: 2/3 + 5/6.
To add these fractions, we need a common denominator, which is 6:
2/3 = 4/6
Now we can add the fractions:
4/6 + 5/6 = 9/6.
Since 9/6 = 1 3/6, we can simplify further:
1 3/6 = 1 1/2.
So, -12 2/3 -(-8 5/6) is equal to 20 1/2.