Use the additive inverse to find −12 2/3 − (−8 5/6). Write the answer as a mixed number.(1 point)
To find the sum of two numbers with opposite signs, you can add their absolute values and give the sum the same sign as the number with the greater absolute value.
First, let's convert both numbers to improper fractions:
−12 2/3 can be written as -12 2/3 = -38/3
−8 5/6 can be written as -8 5/6 = -53/6
Now, we can subtract the second fraction from the first:
-38/3 - (-53/6)
To subtract a negative number, we can change the operation to addition:
-38/3 + 53/6
To add these fractions, we need to find a common denominator, which is 6. So we can multiply the first fraction by 2/2:
(-38/3)(2/2) + 53/6
Simplifying the numerator of the first fraction:
-76/6 + 53/6
Adding the fractions together:
-23/6
To express this as a mixed number, divide the numerator by the denominator:
-23 ÷ 6 = -3 remainder 5
Therefore, the answer is -3 5/6.
To use the additive inverse, we need to change the sign of the second fraction and then add it to the first fraction.
The additive inverse of -8 5/6 is 8 5/6, so we have:
-12 2/3 + 8 5/6
Now, we need to find a common denominator for 3 and 6, which is 6.
Converting -12 2/3 to a fraction with a denominator of 6, we get -74/6.
Converting 8 5/6 to a fraction with a denominator of 6, we get 53/6.
Adding these two fractions, we get:
-74/6 + 53/6
To add the fractions, we keep the denominator the same and add the numerators:
(-74 + 53)/6
-21/6 can be simplified to -3 3/6 or -3 1/2.
Therefore, -12 2/3 - (-8 5/6) is equal to -3 1/2.