Use the additive inverse to find -12 2/3 - (-8 5/6). Write the answer as a mixed number.
To find the sum of -12 2/3 and the additive inverse of -8 5/6, we need to change the sign of -8 5/6 and then add the two numbers.
The additive inverse of a number is simply the number with the opposite sign. So, the additive inverse of -8 5/6 is 8 5/6.
Now, we can add -12 2/3 and 8 5/6.
-12 2/3 + 8 5/6 = (-12 + 8) + (2/3 + 5/6)
Simplifying the whole numbers and adding the fractions separately:
-4 + 3 + (4/6 + 5/6) = -1 + (9/6)
The fraction 9/6 can be simplified to 3/2:
-1 + 3/2 = -1 3/2
Therefore, -12 2/3 - (-8 5/6) is equal to -1 3/2.
To find the sum of -12 2/3 and -(-8 5/6), we will use the additive inverse property, which states that the additive inverse of a number is the number that, when added to the original number, yields a sum of zero.
To change a mixed number to an improper fraction, we multiply the whole number by the denominator and add the numerator. Therefore, -12 2/3 can be written as:
-12 2/3 = - (12 * 3 + 2)/3 = -38/3
Now, we can simplify the expression:
-(-8 5/6) = - (-8) - (5/6) = 8 - (5/6) = 48/6 - 5/6 = 43/6
To subtract two fractions, we need to find a common denominator, which in this case is 6. Therefore, we have:
-38/3 - 43/6
To find the common denominator, we can multiply the denominators of both fractions:
= (-38*2)/(3*2) - (43*1)/(6*1)
= -76/6 - 43/6
Now that the two fractions have the same denominator, we can subtract their numerators and keep the common denominator:
= (-76 - 43)/6
= -119/6
Since the numerator (-119) is greater than the denominator (6), this fraction can be written as a mixed number. To do this, we divide the numerator by the denominator and write the remainder as the numerator of the fractional part:
-119 ÷ 6 = -19 remainder 5
Therefore, the mixed number representation of -119/6 is -19 5/6.
Therefore, the answer, written as a mixed number, is -19 5/6.