A section of a boardwalk is made using 15 boards. Each board is 9 1/4 inches wide. The total width of the section is 144 inches. The spacing between each board is equal. What is the width of the spacing between each board?
The table shows the change in the amount (in gallons) of gasoline in a car over a period of five days. What is the total change in the amount of gasoline in the car over the five day period. Write your answer as a decimal.
Day Change in amount of gasoline (in gallons)
11 −1.05−1.05
22 −1.20−1.20
33 −0.85−0.85
44 10.5010.50
55 −2.15−2.15
The change in the amount of gasoline in the car is
gallons.
If the measurement from the outer edge of the first board to the outer edge of the last board is 144 inches, then there would be 14 spaces between the boards, each measuring 3/8 inch. (14x3/8)+(15x9 1/4)= 144.
Now if this section is in the middle of the boardwalk, there would need to be a space before the first board, making it a total of 15 spaces. Each space would then be 7/20 inch. (15x7/20)+(15x9 1/4)=144.
To find the width of the spacing between each board, we need to subtract the combined width of the boards from the total width of the section.
Step 1: Calculate the combined width of the boards.
The width of one board is 9 1/4 inches. We have 15 boards.
Combined width of the boards = (9 1/4 inches/board) x 15 boards
To multiply the mixed number (9 1/4), convert it to an improper fraction:
(9 1/4) = (36/4 + 1/4) = (37/4)
Combined width of the boards = (37/4) inches/board x 15 boards
To multiply fractions, multiply the numerators and multiply the denominators:
Combined width of the boards = (37 * 15) / (4 * 1) inches
Step 2: Calculate the total width of the section.
The total width of the section is given as 144 inches.
Step 3: Calculate the width of the spacing between each board.
Width of spacing = Total width of the section - Combined width of the boards
Width of spacing = 144 inches - [(37 * 15) / (4 * 1) inches]
Performing the calculation:
Width of spacing = 144 - [(37 * 15) / 4]
Width of spacing = 144 - (555 / 4)
To subtract fractions, make the denominators equal and then subtract the numerators:
Width of spacing = (576 - 555) / 4
Width of spacing = 21 / 4
The width of the spacing between each board is 21/4 inches.
To find the width of the spacing between each board, we first need to determine the total width occupied by the boards. Since there are 15 boards and each board is 9 1/4 inches wide, we can find the total width of the boards by multiplying the number of boards (15) by the width of each board (9 1/4):
Total width of boards = 15 boards × 9 1/4 inches/board
To multiply a whole number by a mixed fraction, we first convert the mixed fraction to an improper fraction. In this case, 9 1/4 can be expressed as 37/4:
Total width of boards = 15 boards × (37/4) inches/board
Next, we can simplify the multiplication:
Total width of boards = (15 × 37) / 4 inches
Now we can calculate the total width of the boards:
Total width of boards = 555/4 inches
Given that the total width of the section is 144 inches, we can find the width of the spacing between each board by subtracting the total width of the boards from the total width of the section:
Width of spacing = Total width of section - Total width of boards
Width of spacing = 144 inches - (555/4) inches
To subtract mixed numbers or fractions, we need to have a common denominator. In this case, the common denominator is 4. We can convert 144 inches to the fraction form:
144 inches = (144/1) inches
Now we can subtract the fractions:
Width of spacing = (144/1) inches - (555/4) inches
To subtract fractions, we need to have the same denominator. We can express 144/1 with a denominator of 4:
Width of spacing = (144/1) * (4/4) - (555/4) inches
Width of spacing = (576/4) - (555/4) inches
Finally, we can subtract the fractions:
Width of spacing = (576 - 555) / 4 inches
Simplifying the numerator:
Width of spacing = 21 / 4 inches
Therefore, the width of the spacing between each board is 21/4 inches, which can be further simplified to 5 1/4 inches.