Final answer:
The weight of a 4(1/2) inch by 5(3/4) inch rectangle of sheet metal, with one square inch weighing 1/8 ounce, is 3 ounces and (15/64) ounces when simplified as a mixed number.
Step-by-step explanation:
To find the weight of a rectangle of sheet metal, where the dimensions are 4(1/2) inches by 5(3/4) inches and one square inch weighs (1/8) ounce, we must first calculate the area of the rectangle and then multiply by the weight per square inch.
The area A of a rectangle is found using the formula A = length × width. Therefore, for our rectangle:
A = 4(1/2) inches × 5(3/4) inches
A = (9/2) inches × (23/4) inches
A = (207/8) square inches
Now, to find the weight, we multiply the area by the weight per square inch:
Weight = (207/8) square inches × (1/8) ounce/square inch
Weight = 207/64 ounces
To simplify the weight, we divide 207 by 64:
Weight = 3 ounces (15/64) ounces
Therefore, the weight of the sheet metal is 3 ounces and (15/64) ounces as a simplified mixed number.