Use the additive inverse to find -12 2/3 - (-8 5/6) write the answer as a mixed number
To find the sum using the additive inverse, we first convert both numbers to improper fractions:
-12 2/3 = -38/3
-8 5/6 = -53/6
Next, we change the subtraction into addition by multiplying the second fraction by -1:
-38/3 + -1 * (-53/6)
Now, we find a common denominator for both fractions, which is 6:
(-38/3) * (2/2) + (53/6) * (1/1)
This simplifies to:
(-76/6) + (53/6)
Adding the numerators:
(-76 + 53)/6
Simplifying further:
-23/6
Lastly, we convert the improper fraction back to a mixed number:
-23/6 = -3 5/6
Therefore, -12 2/3 - (-8 5/6) equals -3 5/6 as a mixed number.
To find the difference between -12 2/3 and -(-8 5/6), we need to subtract the additive inverse of -8 5/6 from -12 2/3.
The additive inverse of -8 5/6 is 8 5/6, so we need to subtract 8 5/6 from -12 2/3.
Converting -12 2/3 to an improper fraction:
-12 2/3 = -((12 * 3) + 2) / 3 = -(36 + 2) / 3 = -38 / 3
Now, we can subtract 8 5/6 from -38/3:
-38/3 - 8 5/6 = -38/3 - ((8 * 6) + 5) / 6 = (-38/3) - (48 + 5)/6 = -38/3 - 53/6
Finding a common denominator:
The common denominator of 3 and 6 is 6, so we need to rewrite -38/3 and -53/6 as fractions with a denominator of 6.
-38/3 = (-38 * 2) / (3 * 2) = -76/6
-53/6 remains the same.
Now, we can subtract the fractions:
-76/6 - 53/6 = (-76 - 53) / 6 = -129/6
Simplifying the fraction:
Dividing both the numerator and denominator by their greatest common divisor (gcd), which is 3,
-129/6 = (-129/3) / (6/3) = -43/2
Therefore, -12 2/3 - (-8 5/6) = -43/2 written as a mixed number is -21 1/2.