Use the additive inverse to find −12 2/3−(−8 5/6). Write the answer as a mixed number.
To find the additive inverse of a number, we change the sign of the number.
First, let's convert −12 2/3 and −8 5/6 to improper fractions:
−12 2/3 = - (12 * 3 + 2) / 3 = -38/3
−8 5/6 = - (8 * 6 + 5) / 6 = -53/6
Now, we can subtract these two fractions:
-38/3 - (-53/6)
To subtract fractions, we need to find a common denominator. The least common multiple (LCM) of 3 and 6 is 6.
Now, we can rewrite the fractions with the common denominator:
-38/3 - (-53/6) = -76/6 + 106/6
Subtracting the fractions:
-76/6 + 106/6 = 30/6 = 5
So, the answer is 5.
To use the additive inverse, we need to change the sign of the second fraction and then add the two fractions together.
The additive inverse of −8 5/6 is 8 5/6.
Now we can add −12 2/3 and 8 5/6 together:
−12 2/3 + 8 5/6 = (−12 + 8) + (2/3 + 5/6)
−12 + 8 = -4
To add the fractions 2/3 and 5/6, we need a common denominator.
The common denominator of 3 and 6 is 6.
Converting 2/3 to have a denominator of 6, we get 4/6.
Now we can add the fractions:
2/3 + 5/6 = 4/6 + 5/6 = 9/6
Simplifying the fraction, we have:
9/6 = 3/2
Putting it all together, we have:
−12 2/3 + 8 5/6 = -4 + 3/2
Now, to write the answer as a mixed number, we can convert the fraction 3/2 into a mixed number:
3 ÷ 2 = 1 remainder 1
Therefore, the mixed number is:
−4 + 1 1/2
So, −12 2/3−(−8 5/6) = −4 + 1 1/2.