Derek is building a bird feeder to sell at a crafts fair. He is using a board that is 4 feet long. He will cut one piece that is 2 feet long for the base. Then he will use the rest of the board and cut it into two pieces of equal length for the sides. If he puts the and one of the sides together first, what fraction of the total board will he have used?
This doesn't make much sense. Please correct this sentence and repost.
If he puts the and one of the sides together first, what fraction of the total board will he have used?
Ms. Sue,
Sorry. The question is If he puts the base and one of the sides together first, what fraction of the total board will he have used?
3/4
Can you please show me how to work out the problem so that I can understand it?
He started with a 4-foot piece. He then cut off 2 feet, leaving a 2-foot piece. 2/4 = 1/2 remains.
He used 1/2 of what was left.
1/2 * 1/2 = 1/4
4/4 - 1/4 = 3/4
Thanks Ms. Sue!
To find the fraction of the total board that Derek will have used, we need to determine the total length of the board and the length of the parts he will use.
First, Derek cuts a 2-feet long piece for the base. Then, he uses the remaining part of the board to cut two equal-length pieces for the sides.
Since the board was initially 4 feet long, and he used 2 feet for the base, he has 4 - 2 = 2 feet remaining for the sides.
Since he needs two equal-length pieces for the sides, each piece will be 2/2 = 1 foot long.
Therefore, Derek will have used a total of 2 + 1 + 1 = 4 feet of the board.
The total length of the board is 4 feet, and Derek used 4 feet of that board, so the fraction of the total board that he used is 4/4, which simplifies to 1.
Therefore, Derek will have used the entire board, which can be expressed as the fraction 1/1.