Mr. Johnston needs a shelf to hold a set of textbooks, each 1 3/4 in. wide. How many books will fit on a shelf that is 35 in long?
Mae -- please use the same name for your posts.
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To determine how many books will fit on a shelf, we need to divide the length of the shelf by the width of each book.
In this case, the length of the shelf is 35 inches.
The width of each book is given as 1 3/4 inches. To convert this mixed number into an improper fraction, we can multiply the whole number (1) by the denominator (4) and add the resulting product (4) to the numerator (3) to get 7. So, the width of each book is 7/4 inches.
Now, we can divide the length of the shelf by the width of each book to find the number of books that will fit on the shelf:
35 inches ÷ (7/4) inches/book
To divide fractions, we can multiply the first fraction by the reciprocal of the second fraction:
35 inches ÷ (7/4) inches/book = 35 inches × (4/7 inches/book)
Now, we can simplify the expression by canceling out common factors:
35 inches × (4/7 inches/book) = 140/7 inches
Dividing 140 by 7, we get:
140/7 inches = 20 books
So, Mr. Johnston can fit 20 books on the shelf.