A nail that is 2 1 ⁄ 2 inches long is hammered through three boards, each of which is 5/8 inch thick. How much of the nail is sticking out the opposite side. Show set-up and support. Please help ASAP!!! :(
5/8 * 3 = 15/8
So, subtract that from 2 1/2 = 20/8
To calculate how much of the nail is sticking out the opposite side, we need to find the total thickness of the three boards and subtract it from the length of the nail. Here is the step-by-step set-up and solution:
1. Determine the length of the nail: The nail is stated to be 2 1/2 inches long. To work with fractions, we need to convert this to an improper fraction. The fraction 2 1/2 can be written as 5/2. So, the length of the nail is 5/2 inches.
2. Determine the thickness of each board: Each board is stated to be 5/8 inch thick.
3. Calculate the total thickness of the three boards: To find this, we need to multiply the thickness of one board (5/8 inch) by the number of boards (3). Multiply the numerator (5) by 3, which equals 15. The denominator remains the same: 8. So, the total thickness of the three boards is 15/8 inch.
4. Calculate the remaining length of the nail sticking out: To find this, subtract the total thickness of the three boards from the length of the nail. Subtract the fraction 15/8 inch from the fraction 5/2 inch.
To subtract fractions, we need to find a common denominator. The common denominator for 8 and 2 is 8. Therefore, we rewrite the fractions with the common denominator:
5/2 inch = 20/8 inch
15/8 inch = 15/8 inch
Now, subtract the fractions: 20/8 inch - 15/8 inch = (20 - 15) / 8 inch = 5/8 inch
The remaining length of the nail sticking out the opposite side is 5/8 inch.
That's it! The nail is sticking out 5/8 inch on the opposite side after being hammered through the three boards.