a library shelf is 9 ft wide. a set of books fills 1/6 of the shelf space.each book in the set is 3/5 inch thick. how many books are in the set?
I have tried working this fraction problem and I am stuck
The total shelf space is 9 feet wide.
But the set of books uses only 1/6 of the space. Therefore, the space used = 9*1/6 = 9/6 = 3/2 ft
Each book is 3/5 inches thick. First, you have to get both terms in the same units. There are 12in in 1 ft, so multiply the 3/2 ft by 12 to find the number of inches. 3/2 * 12 = 18.
Now divide 18in by 3/5in. 18/(3/5) = 18*(5/3) = 30 books
To find out how many books are in the set, we will first calculate the total thickness of the books that fill 1/6 of the shelf space.
The width of the shelf is given as 9 ft.
Since 1 foot is equal to 12 inches, the width of the shelf in inches is:
9 ft * 12 inches/ft = 108 inches
Next, we know that the set of books fills 1/6 of the shelf space.
To find the thickness of this set, we multiply the width of the shelf by 1/6:
108 inches * 1/6 = 18 inches
Now, we know that each book in the set is 3/5 inch thick.
To find the number of books in the set, we divide the total thickness of the set by the thickness of each book:
18 inches / (3/5 inch/book)
To divide by a fraction, we can multiply by its reciprocal:
18 inches * (5/3 inch/book)
Cancel out the inches:
6 * 5 book/1 * 1/3
Multiply the numbers:
30 books / 3
Divide:
30 books / 3 = 10 books
Therefore, there are 10 books in the set.
To find the number of books in the set, you first need to determine the total available space on the shelf and then divide it by the thickness of each book to get the number of books.
Given information:
- Width of the library shelf: 9 ft
- Shelf space filled by the set of books: 1/6 of the shelf
- Thickness of each book: 3/5 inch
Step 1: Convert the width of the shelf to inches.
1 foot = 12 inches (since there are 12 inches in a foot)
9 ft * 12 inches/ft = 108 inches
Step 2: Calculate the total available space on the shelf for the set of books.
Total space on the shelf = 108 inches
Space filled by the set of books = 1/6 of the shelf space
To find the space filled by the set of books, divide the total space on the shelf by 6:
Space filled by the set of books = (1/6) * 108 inches = 18 inches
Step 3: Determine the number of books in the set.
Since each book is 3/5 inch thick, divide the space filled by the set of books by the thickness of each book:
Number of books = (Space filled by the set of books) / (Thickness of each book)
Number of books = 18 inches / (3/5) inch
To divide by a fraction, multiply by its reciprocal:
Number of books = 18 inches * (5/3 inch)
Number of books = 90/3 = 30 books
Therefore, there are 30 books in the set.