In his den, Matt wants to build two shelves. One shelf is to measure four and three over4 3/4 feet long and the other five and 5 5/12 feet long. Is a board 11 feet long enough for both shelves

10¹/₆ feet is less than 11 feet board, it's enough for both shelves

Step-by-step explanation:

First shelf is to measure = 4³/₄ feet

Second shelf is to measure = 5⁵/₁₂ feet

Total length of available board = 11 feet

Hence length of 1st and 2nd shelves are added to determine if its less than or equal to 11 feet

Length of 1st and 2nd shelves = 4³/₄ + 5⁵/₁₂ = 122/12 feet = 10¹/₆ feet

10¹/₆ feet is less than 11 feet board, it's enough for both shelves