Use the additive inverse to find -12 and 2/3 - (-8 and 5/6). Write the answer as a mixed number.
To find the additive inverse of a number, you simply change the sign of the number.
The additive inverse of -12 is 12.
To find (-12) + (2/3) - (-8) - (5/6), we need to simplify the expression.
(-12) + (2/3) - (-8) - (5/6) = 12 + (2/3) + 8 - (5/6)
To add fractions, we need a common denominator. Since the denominators are 3 and 6, we can multiply the numerator and denominator of (2/3) by 2 to get a common denominator of 6.
12 + (2/3) + 8 - (5/6) = 12 + (4/6) + 8 - (5/6)
Now the fractions have a common denominator and we can add the numerators.
12 + (4/6) + 8 - (5/6) = 12 + (4 + 8 - 5)/6
Simplifying the numerator further:
12 + (4 + 8 - 5)/6 = 12 + (7/6)
Now we need to convert the improper fraction 7/6 into a mixed number.
7 divided by 6 is equal to 1 with a remainder of 1. So, 7/6 = 1 and 1/6.
Substituting back into the expression:
12 + (7/6) = 12 + 1 and 1/6
The final answer as a mixed number is 13 and 1/6.
To find the difference using the additive inverse, we will subtract the second number from the first number. We have:
-12 - (2/3) - (-8 and 5/6)
First, we need to convert -12 into a mixed number. Since it's already a negative whole number, we can simply write it as -12 and 0/1.
Next, we need to convert -8 and 5/6 into an improper fraction. To do this, we multiply the whole number (-8) by the denominator (6) and add the numerator (5):
-8 * 6 + 5 = -48 + 5 = -43
So, -8 and 5/6 can be written as -43/6.
Now, we can subtract by finding the common denominator:
-12 and 0/1 - (-43/6)
To find the common denominator, we multiply the denominators together:
1 * 6 = 6
Now, we can rewrite -12 and 0/1 as an improper fraction:
-12 * 6 + 0 = -72 + 0 = -72
So, -12 and 0/1 can be written as -72/6.
Now, we can subtract:
-72/6 - (-43/6)
To subtract, we simply subtract the numerators:
-72 - (-43) = -72 + 43 = -29
So, the result is -29/6.
To convert this improper fraction into a mixed number, we divide the numerator (-29) by the denominator (6):
-29 ÷ 6 = -4 remainder 2
Therefore, the answer as a mixed number is -4 and 2/6.
Simplifying the fraction, we can reduce 2/6:
2/6 = 1/3
So, the final answer is -4 and 1/3.