Final answer:
To find the combined length of buttons longer than 1 inch, add the lengths of the buttons and simplify the fraction.
Step-by-step explanation:
To find the combined length of all buttons longer than 1 inch, we need to add the lengths of the two buttons. The first button is 1 1/8 inch long, which can be written as 1 + 1/8 = 8/8 + 1/8 = 9/8 inches. The second button is 1 1/4 inch long, which can be written as 1 + 1/4 = 4/4 + 1/4 = 5/4 inches. Adding these two lengths together, we get 9/8 + 5/4 = 18/16 + 20/16 = 38/16 inches. Simplifying this fraction, we get 2 6/16 inches, which can be further simplified to 2 3/8 inches. Therefore, the combined length of the buttons longer than 1 inch is 2 3/8 inches.