Use the additive inverse to find -12 2/3 - -8 5/6 Write the answer as a mixed number.
To find the difference between the two numbers -12 2/3 and -8 5/6 using the additive inverse, we need to change the second number into its additive inverse and then add the two numbers together.
The additive inverse of -8 5/6 is the opposite sign of the number, so it will become positive. Thus, the additive inverse of -8 5/6 is 8 5/6.
Now we can subtract -12 2/3 from 8 5/6.
8 5/6 - 12 2/3
Let's first make the denominators the same. The common denominator of 6 and 3 is 6.
To convert 8 5/6 to the same denominator of 6, we multiply the whole number (8) by 6 and add that to the numerator (5). This gives us 53/6.
Now we have:
53/6 - 12 2/3
Next, let's convert the mixed number 12 2/3 to an improper fraction.
To do this, we can multiply the whole number (12) by the denominator (3) and add that to the numerator (2). This gives us 38/3.
Now we have:
53/6 - 38/3
To subtract these fractions, we need to have the same denominator. The common denominator of 6 and 3 is 6, so we can multiply the numerator and denominator of the second fraction by 2 to get the same denominator of 6.
Doing this, we have:
53/6 - (38*2)/(3*2)
53/6 - 76/6
Now that the denominators are the same, we can subtract the numerators:
(53 - 76) / 6
53 - 76 = -23
So, we have:
-23/6
To convert this improper fraction to a mixed number, we divide the numerator (-23) by the denominator (6) and express the remainder as a fraction.
-23 ÷ 6 = -3 remainder 5 (or -3 with a remainder of 5)
Therefore, the difference -12 2/3 - -8 5/6 as a mixed number is -3 5/6.
To find the sum, we subtract the second operand (the negative term) from the first operand:
-12 2/3 - (-8 5/6)
The additive inverse of -8 5/6 is 8 5/6. So, we can rewrite the expression as:
-12 2/3 + 8 5/6
To perform addition, we need to have a common denominator for the two fractions:
The common denominator is 6, so we convert -12 2/3 and 8 5/6 to fractions with denominators of 6.
-12 2/3 = -38/3
8 5/6 = 53/6
Now, we can add the two fractions together:
-38/3 + 53/6
To add these fractions, we need to have a common denominator. The least common multiple of 3 and 6 is 6.
So, we convert the fractions to have a denominator of 6:
(-38/3) * (2/2) = -76/6 = -38/3
53/6
Now that the fractions have a common denominator, we can add them together:
-38/3 + 53/6 = (-38 + 53)/6 = 15/6
Next, we simplify the resulting fraction:
15/6 = 5/2
Since the fraction is larger than 1, we can rewrite it as a mixed number:
5/2 = 2 1/2
Therefore, -12 2/3 - -8 5/6 equals 2 1/2.