Use the additive inverse to find -12 2/3 Minus (-8 5/6). Write the answer as a mixed number

Answer 1

To solve \(-12 \frac{2}{3} - (-8 \frac{5}{6})\) using the additive inverse, we first rewrite the equation:

\[ -12 \frac{2}{3} + 8 \frac{5}{6} \]

Next, we convert each mixed number to an improper fraction:

1. Convert \(-12 \frac{2}{3}\): \[ -12 \frac{2}{3} = -\left(12 \times 3 + 2\right) = -\left(36 + 2\right) = -\frac{38}{3} \]

2. Convert \(8 \frac{5}{6}\): \[ 8 \frac{5}{6} = 8 \times 6 + 5 = 48 + 5 = \frac{53}{6} \]

Now, we can rewrite the expression as:

\[ -\frac{38}{3} + \frac{53}{6} \]

To add these fractions, we need a common denominator. The least common multiple of 3 and 6 is 6. We convert \(-\frac{38}{3}\) to a fraction with a denominator of 6:

\[ -\frac{38}{3} = -\frac{38 \times 2}{3 \times 2} = -\frac{76}{6} \]

Now the expression becomes:

\[ -\frac{76}{6} + \frac{53}{6} \]

Now we can combine the fractions:

\[ \frac{-76 + 53}{6} = \frac{-23}{6} \]

Now, we convert \(-\frac{23}{6}\) back to a mixed number. Since \(-23\) divided by \(6\) gives us \(-3\) with a remainder of \(5\), we have:

\[ -\frac{23}{6} = -3 \frac{5}{6} \]

Thus, the final answer is:

\[ \boxed{-3 \frac{5}{6}} \]

Answer 2

Dont put it in weird text

Answer 3

Sure! Let's break it down step-by-step without any complex formatting.

We need to calculate:

-12 2/3 - (-8 5/6)

First, we change the subtraction of a negative into addition:

-12 2/3 + 8 5/6

Now, let's convert the mixed numbers into improper fractions:

1. Convert -12 2/3:

   • 12 * 3 + 2 = 36 + 2 = 38
   • So, -12 2/3 = -38/3

2. Convert 8 5/6:

   • 8 * 6 + 5 = 48 + 5 = 53
   • So, 8 5/6 = 53/6

Now we have:

-38/3 + 53/6

Next, we need a common denominator to add these fractions. The least common multiple of 3 and 6 is 6.

Convert -38/3 to have a denominator of 6:

-38/3 = -76/6 (since -38 * 2 = -76)

Now we can add the fractions:

-76/6 + 53/6 = (-76 + 53)/6 = -23/6

Finally, convert -23/6 back to a mixed number:

-23/6 = -3 5/6 (since 23 divided by 6 is 3 with a remainder of 5)

So the final answer is:

-3 5/6