use the additive inverse to find -12 2/3 - (-8 5/6)
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 simply -8 5/6 itself. To subtract -8 5/6, we change the operation to addition and negate the value:
-12 2/3 + 8 5/6
Next, we need to convert the mixed numbers into improper fractions:
-12 2/3 = -(38/3)
8 5/6 = 53/6
Now we can subtract the fractions:
-(38/3) + (53/6)
To add fractions, we need a common denominator. The least common multiple of 3 and 6 is 6.
Converting both fractions to have a denominator of 6:
-(38/3) = -((38/3) * (2/2)) = -76/6
(53/6) stays the same
Now we can add the fractions:
-76/6 + 53/6 = (-76 + 53)/6 = -23/6
Therefore, -12 2/3 - (-8 5/6) = -23/6 or -3 5/6.
To use the additive inverse to find the subtraction of -12 2/3 - (-8 5/6), you first need to change the subtraction into addition by changing the sign of the second number.
-12 2/3 - (-8 5/6) becomes -12 2/3 + 8 5/6.
Next, you need to find the least common denominator (LCD) of the fractions, which in this case is 6.
Converting the mixed numbers into improper fractions:
-12 2/3 = -38/3
8 5/6 = 53/6
Now, we can add the two fractions:
-38/3 + 53/6
To add these fractions, we need to make their denominators the same, which is 6.
Multiply the numerator and denominator of the first fraction by 2 to get a common denominator:
-38/3 * (2/2) = -76/6
Now, we can add the two fractions:
-76/6 + 53/6 = -23/6
Therefore, -12 2/3 - (-8 5/6) is equal to -23/6.