-12 2/3 - (-8 5/6)?
To subtract mixed numbers, you first need to change them to improper fractions.
-12 2/3 can be written as -38/3.
-8 5/6 can be written as -53/6.
Now, to subtract them, you can subtract the numerators while keeping the same denominator: -38/3 - (-53/6).
To subtract a negative number, you need to change the operation to addition: -38/3 + 53/6.
Now, since the denominators are different, you need to find a common denominator. In this case, the least common multiple of 3 and 6 is 6.
So, you need to multiply -38/3 by 2/2 to get -76/6.
Now, the expression becomes -76/6 + 53/6.
Now, you can subtract the numerators while keeping the same denominator: -76 + 53 = -23.
The final answer is -23/6.
To subtract mixed numbers, we need to convert them into improper fractions.
For -12 2/3:
Multiply the whole number (-12) by the denominator of the fraction (3), then add the numerator (2). Place the result over the original denominator.
-12 x 3 + 2 = -36 + 2 = -34
So, -12 2/3 can be written as -34/3.
For -8 5/6:
Multiply the whole number (-8) by the denominator of the fraction (6), then add the numerator (5). Place the result over the original denominator.
-8 x 6 + 5 = -48 + 5 = -43
So, -8 5/6 can be written as -43/6.
Now we can subtract the two fractions.
-34/3 – (-43/6)
To subtract fractions, we need a common denominator.
The least common multiple (LCM) of 3 and 6 is 6.
To convert -34/3 to a fraction with a denominator of 6, multiply both the numerator and denominator by 2.
(-34 x 2)/(3 x 2) = -68/6
So, the expression becomes:
-68/6 - (-43/6)
Now, we can subtract the fractions:
-68/6 - (-43/6) = -68/6 + 43/6
To add fractions, we add the numerators and keep the denominators the same:
-68/6 + 43/6 = (-68 + 43)/6 = -25/6
So, -12 2/3 - (-8 5/6) is equal to -25/6.