−12 2/3−(−8 5/6). Write the answer as a mixed number.(1 point)
To solve this subtraction problem, we need to find the common denominator of the two fractions involved. In this case, the common denominator is 6.
We can rewrite -12 2/3 as an improper fraction:
-12 2/3 = -38/3
Similarly, we can rewrite -8 5/6 as an improper fraction:
-8 5/6 = -53/6
Subtracting these two fractions:
-38/3 - (-53/6)
To subtract fractions, we need to have a common denominator. In this case, the common denominator is 6.
-38/3 = -76/6
Now we can subtract the fractions:
-76/6 - (-53/6) = - (76/6 + 53/6) = - (129/6)
Simplifying the fraction by dividing both the numerator and denominator by the greatest common divisor, which is 3, we get:
- (129/6) = -43/2
Now we can rewrite -43/2 as a mixed number:
-43/2 = -21 1/2
Therefore, the answer is -21 1/2.
To subtract mixed numbers, we first need to convert each mixed number into an improper fraction.
For −12 2/3, we can convert it into an improper fraction by multiplying the whole number part (-12) by the denominator (3) and adding the numerator (2), then writing the result over the denominator:
-12 * 3 + 2 = -36 + 2 = -34
So, −12 2/3 as an improper fraction is -34/3.
For −8 5/6, we can convert it into an improper fraction using the same process:
-8 * 6 + 5 = -48 + 5 = -43
So, −8 5/6 as an improper fraction is -43/6.
Now we can subtract these two improper fractions:
-34/3 - (-43/6)
To subtract fractions, we need to find a common denominator. The least common multiple of 3 and 6 is 6. So, we can rewrite the fractions with the common denominator of 6:
-34/3 = -34/3 * 2/2 = -68/6
-43/6
Now, we can subtract the numerators and keep the common denominator:
-68/6 - (-43/6) = -68/6 + 43/6 = (-68 + 43)/6 = -25/6
The answer, written as a mixed number, is:
-25/6 = -4 1/6