1). How many shelves each 2 3/4 feet in length can be cut from a piece of lumber that is 15 2/3 feet long?
15 2/3 = 47/3
2 3/4 = 11/4
(47/3) / (11/4)
(47/3) * (4/11) = 188/33 = 5.7 = 5 shelves
To find out how many shelves can be cut from a piece of lumber, we need to divide the length of the lumber by the length of each shelf.
First, let's convert the given lengths to a common fraction to make calculations easier:
- 2 3/4 feet = (8/4 + 3/4) feet = 11/4 feet
- 15 2/3 feet = (47/3) feet
Next, we will perform the division to find the number of shelves:
(47/3) feet ÷ (11/4) feet = (47/3) feet × (4/11) feet
To multiply fractions, we multiply their numerators and denominators:
(47 × 4) / (3 × 11) = 188/33
Therefore, you can cut 188/33 shelves from a piece of lumber that is 15 2/3 feet long.