Final answer:
To represent the overall change in Mr. Yoo's weight using signed numbers, we add the weight lost (-12) and the weight gained (+5⅜), resulting in an overall change of -45/8 pounds.
Step-by-step explanation:
To represent the situation of Mr. Yoo's weight change, we can use the concept of signed numbers. Let's assign a positive sign for weight gained and a negative sign for weight lost. So, Mr. Yoo losing 12 pounds over the summer can be represented as -12, and him gaining 5⅜ pounds by winter can be represented as +5⅜.
To find the overall change in Mr. Yoo's weight, we can add these two signed numbers: -12 + 5⅜. To perform the addition, we need to convert 5⅜ to an improper fraction: +5⅜ = +5 + ⅜ = +5 + 8/8 + 3/8 = +5 + 11/8. Now we can add -12 and +5 + 11/8: -12 + 5 + 11/8 = (-12 + 5) + 11/8 = -7 + 11/8. To simplify the sum, we need a common denominator, which is 8: -7 + 11/8 = -56/8 + 11/8 = -45/8.
Therefore, the overall change in Mr. Yoo's weight is -45/8 pounds.