Final answer:
To complete the equation 8 4/5 - 2/3 + _ = 3 1/10, convert all numbers to fractions with a common denominator. The resulting equation after obtaining common denominators and performing the subtraction is 8 4/5 - 2/3 - 4 = 3 1/10, thus the missing number is -4.
Step-by-step explanation:
To find the missing number that completes the equation 8 4/5 - 2/3 + _ = 3 1/10, we need to combine the given numbers and solve for the blank. Start by converting the mixed number 8 4/5 to an improper fraction, which is 44/5. Then, subtract 2/3 from 44/5. To subtract, we need a common denominator, which would be 15 in this case.
Convert 44/5 and 2/3 to have the common denominator of 15, obtaining 132/15 and 10/15 respectively. Subtracting them gives us 122/15. Now, we need to determine what added to 122/15 equals 3 1/10. First, convert 3 1/10 to an improper fraction, which is 31/10. Convert this to have the common denominator of 15, giving us 93/30 or 62/15.
We solve for the missing number by subtracting 122/15 from 62/15, resulting in the missing value being -60/15, which simplifies to -4. Thus, the complete equation is 8 4/5 - 2/3 - 4 = 3 1/10.