1.Why do you multiply to change from a larger unit to a smaller unit?
2. A carpenter cuts 2 ft 9 in. off a board that has 4 ft long. How long is the piece that is left , in feet and inches?
larger unit = foot
smaller unit = inch -- more inches than feet in the same length
2.
4 - 2 ft, 9 in = 3 ft. 12 in - 2 ft, 9 in = ?
1. When converting from a larger unit to a smaller unit, you multiply because each unit contains a certain number of the smaller units. By multiplying by the conversion factor, you are essentially "cancelling out" the larger unit and converting the value into the equivalent amount of smaller units.
For example, if you want to convert 4 feet to inches, you know that 1 foot is equal to 12 inches. Therefore, you multiply 4 feet by the conversion factor of 12 inches per foot:
4 feet * 12 inches/foot = 48 inches
By multiplying the number of feet by 12, you are effectively multiplying it by the number of inches in 1 foot, giving you the equivalent length in inches.
2. To find the length of the piece that is left after the carpenter cuts off 2 ft 9 in. from a 4 ft long board, you need to perform subtraction and conversion.
First, let's convert 2 ft 9 in. to inches. Since 1 foot is equal to 12 inches, we have:
2 ft * 12 inches/foot + 9 inches = 24 inches + 9 inches = 33 inches
So, the length that was cut off is 33 inches.
To find the length of the remaining piece, we subtract the length that was cut off from the original length of the board:
4 ft * 12 inches/foot - 33 inches = 48 inches - 33 inches = 15 inches
Therefore, the piece that is left is 15 inches long. However, if you want to express it in feet and inches, you need to convert it back. Since 1 foot is equal to 12 inches, we can divide the 15 inches by 12 to get the number of feet:
15 inches / 12 inches/foot = 1.25 feet
So, the piece that is left is 1 foot 3 inches long.