-12 2/3 - 8 5/6
To solve -12 2/3 - 8 5/6, we need to first find a common denominator for the fractions. In this case, the denominator for 2/3 is 3 and the denominator for 5/6 is 6.
To make the denominators the same, we can multiply the fraction 2/3 by 2/2 to become 4/6. Similarly, we can multiply the fraction 5/6 by 1/1 to remain the same, 5/6.
So now we have -12 4/6 - 8 5/6.
Notice that 4/6 is equivalent to 2/3. Therefore, we can rewrite the equation as -12 2/3 - 8 5/6.
Next, we subtract 2/3 from 5/6. To do this, we need to find a common denominator. The least common multiple of 3 and 6 is 6.
To make the denominators the same, we can multiply the fraction 2/3 by 2/2 to become 4/6.
So now we have -12 4/6 - 8 4/6.
We can now subtract the fractions: 5/6 - 4/6 = 1/6.
Taking away the whole numbers: -12 - 8 = -20.
So the final answer is -20 1/6.
To subtract mixed fractions, follow these steps:
Step 1: Convert the mixed numbers to improper fractions.
Convert -12 2/3 to an improper fraction:
-12 2/3 = (-12 × 3 + 2)/3 = (-36 + 2)/3 = -34/3.
Convert 8 5/6 to an improper fraction:
8 5/6 = (8 × 6 + 5)/6 = (48 + 5)/6 = 53/6.
Step 2: Find a common denominator.
The denominators of -34/3 and 53/6 are 3 and 6, respectively.
The common denominator of 3 and 6 is 6.
Step 3: Adjust the numerators.
To adjust the numerators, multiply the numerator and denominator of each fraction by the same number so their denominators become the same (in this case, 6).
For -34/3, multiply the numerator and denominator by 2:
(-34 × 2)/(3 × 2) = -68/6.
For 53/6, no adjustment is needed.
Step 4: Subtract the numerators and keep the common denominator.
Now that the denominators are the same, subtract the numerators and keep the common denominator:
-68/6 - 53/6 = (-68 - 53)/6 = -121/6.
Step 5: Simplify the result, if necessary.
The result, -121/6, is an improper fraction. If you want to express this as a mixed number, divide the numerator (121) by the denominator (6):
121 ÷ 6 = 20 remainder 1.
So, the result as a mixed number is:
-121/6 = -20 1/6.
Therefore, -12 2/3 - 8 5/6 = -20 1/6.