Noah has a piece of lumber that is 5 ½
feet long. He needs to cut it into pieces.
that are 2/3 long. How many pieces can he?
cut from this board? Will he have any wood left over?
To find out how many pieces Noah can cut from the board, we need to divide the length of the board by the length of each piece.
Length of the board: 5 ½ feet = 5 + 1/2 = 10/2 + 1/2 = 11/2 feet
Length of each piece: 2/3 feet
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
Number of pieces = (11/2) / (2/3)
= (11/2) * (3/2)
= (11 * 3) / (2 * 2)
= 33/4
So Noah can cut 33/4 pieces from the board.
To check if Noah will have any wood left over, we need to find the remainder when the length of the board is divided by the length of each piece.
Remainder = (11/2) % (2/3)
= (11/2) - (2/3) * (33/4)
= 11/2 - 2/3 * 33/4
= 11/2 - 2/1 * 1/4
= 11/2 - 1/2
= 10/2
= 5/1
= 5 feet
So Noah will have 5 feet of wood left over.