The ratio of new books to all books is 5:12.
In this scenario, there are 5 new books and 7 used books on a shelf. We will determine the ratio of new books to all books and explain it mathematically.
To find the ratio of new books to all books, we need to compare the number of new books to the total number of books, which includes both new and used books. In this case, there are 5 new books and 7 used books, so the total number of books is 5 + 7 = 12.
Now, let's define the ratio of new books to all books using the mathematical notation. We'll use "n" to represent the number of new books, "u" to represent the number of used books, and "t" to represent the total number of books.
Let:
n = 5 (number of new books)
u = 7 (number of used books)
t = n + u = 5 + 7 = 12 (total number of books)
The ratio of new books to all books is given by n/t. Substituting the values, we get:
Ratio of new books to all books = 5 / 12
The ratio can also be expressed in fractional form as 5/12. This means that out of every 12 books on the shelf, 5 are new books, and the remaining 7 are used books. The ratio is simplified to its lowest terms, making it a concise representation of the relationship between new books and all books on the shelf.
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