-12 2/3 - -8 5/6
To simplify the expression -12 2/3 - (-8 5/6), you need to change the mixed numbers to improper fractions and then perform the subtraction.
Converting -12 2/3 to an improper fraction:
-12 is the whole number and 2/3 is the fractional part.
To convert the whole number to a fraction, multiply the denominator (3) by the whole number (-12) and add the numerator (2):
-12 * 3 = -36
-36 + 2 = -34
So, -12 2/3 can be written as -34/3.
Converting -8 5/6 to an improper fraction:
-8 is the whole number and 5/6 is the fractional part.
To convert the whole number to a fraction, multiply the denominator (6) by the whole number (-8) and add the numerator (5):
-8 * 6 = -48
-48 + 5 = -43
So, -8 5/6 can be written as -43/6.
Now, we can substitute these fractions into the expression:
-34/3 - (-43/6)
To subtract fractions, you need a common denominator. The common denominator for 3 and 6 is 6.
Converting -34/3 to an equivalent fraction with the denominator 6:
Multiply the numerator (-34) and the denominator (3) by 2:
-34 * 2 = -68
3 * 2 = 6
-68/6
So, the expression becomes:
-68/6 - (-43/6)
To subtract fractions with the same denominator, subtract the numerators and keep the denominator:
(-68 - (-43))/6
Simplifying the numerator:
-68 + 43 = -25
So, the expression simplifies to:
-25/6
To subtract mixed numbers, follow these steps:
Step 1: Convert the mixed numbers into improper fractions.
-12 2/3 = -12 + 2/3
= (-12 * 3)/3 + 2/3
= -36/3 + 2/3
= (-36 + 2)/3
= -34/3
-8 5/6 = -8 + 5/6
= (-8 * 6)/6 + 5/6
= -48/6 + 5/6
= (-48 + 5)/6
= -43/6
Step 2: Perform the subtraction of the fractions.
-34/3 - (-43/6)
Step 3: To subtract fractions, find a common denominator.
The common denominator for 3 and 6 is 6.
Step 4: Rewrite the fractions with the common denominator.
-34/3 = -34/3 * 2/2
= -68/6
Step 5: Subtract the fractions.
-68/6 - (-43/6)
= -68/6 + 43/6
= (-68 + 43)/6
= -25/6
Step 6: Simplify the fraction if necessary.
-25/6 is already simplified.
Therefore, -12 2/3 - (-8 5/6) = -25/6.