Question
Use the additive inverse to find -12 2/3--8 5/6 write the answer as a mixed number
Answers
GPT 3.5
To find the sum of -12 2/3 and -8 5/6 using the additive inverse, we can change the sign of the second number and then add it to the first number.
First, we need to change the sign of -8 5/6. The whole number part is 8 and the mixed fraction is 5/6. Changing the sign of a mixed fraction involves changing the sign of the whole number and the fraction as well. Thus we have:
-8 5/6 = -8 - 5/6 = -8 - (5/6) = -8 - (5/6) = -8 - 5/6 = -8 - 5/6 = -48/6 - 5/6 = -53/6
Now we can simply add -12 2/3 to -53/6:
-12 2/3 + (-53/6)
To add these, we need a common denominator. Since the denominators are already multiples of each other, we can simply use the product of the two denominators, which is 3 x 6 = 18.
Converting -12 2/3 to an improper fraction:
-12 2/3 = -12(3/3) + 2/3 = -36/3 + 2/3 = -34/3
Now we can add:
-34/3 + (-53/6) = (-34*6)/(3*6) + (-53*3)/(6*3) = -204/18 - 159/18 = (-204 - 159)/18 = -363/18
Simplifying -363/18, we can divide numerator and denominator by their greatest common divisor, which is 9:
-363/18 = -363/9 / 18/9 = -363/9 / 2 = -363/9 * 1/2 = (-363 * 1)/(9 * 2) = -363/18 = -121/6
Therefore, the sum of -12 2/3 and -8 5/6 as a mixed number is -121/6 which can be written as -20 1/6
First, we need to change the sign of -8 5/6. The whole number part is 8 and the mixed fraction is 5/6. Changing the sign of a mixed fraction involves changing the sign of the whole number and the fraction as well. Thus we have:
-8 5/6 = -8 - 5/6 = -8 - (5/6) = -8 - (5/6) = -8 - 5/6 = -8 - 5/6 = -48/6 - 5/6 = -53/6
Now we can simply add -12 2/3 to -53/6:
-12 2/3 + (-53/6)
To add these, we need a common denominator. Since the denominators are already multiples of each other, we can simply use the product of the two denominators, which is 3 x 6 = 18.
Converting -12 2/3 to an improper fraction:
-12 2/3 = -12(3/3) + 2/3 = -36/3 + 2/3 = -34/3
Now we can add:
-34/3 + (-53/6) = (-34*6)/(3*6) + (-53*3)/(6*3) = -204/18 - 159/18 = (-204 - 159)/18 = -363/18
Simplifying -363/18, we can divide numerator and denominator by their greatest common divisor, which is 9:
-363/18 = -363/9 / 18/9 = -363/9 / 2 = -363/9 * 1/2 = (-363 * 1)/(9 * 2) = -363/18 = -121/6
Therefore, the sum of -12 2/3 and -8 5/6 as a mixed number is -121/6 which can be written as -20 1/6