Juan has measured the location of his bookcase and realized that he could only fit a bookcase with shelves that are 1 3/4 feet wide. what is the maximum number of shelves Juan could build for a new bookcase using 18 ft of lumber.

18/1.75 = ?

18/(7/4)

18* 4/7
72/4 = 10 2/7

I don't understand how to figure this question out ??? Help please!

10 shelves

To find the maximum number of shelves Juan could build for a new bookcase, we need to determine how many 1 3/4 feet wide shelves can fit within 18 feet of lumber.

Step 1: Convert 1 3/4 feet to an improper fraction.
1 3/4 = (4 * 1 + 3)/4 = 7/4 feet

Step 2: Divide the total length of the lumber (18 feet) by the width of each shelf (7/4 feet).
18 feet ÷ (7/4 feet) = 18 feet × (4/7 feet)

Step 3: Multiply the numerators and denominators.
18 × 4 = 72
7 × 1 = 7

Step 4: Divide the resulting numerator by the resulting denominator.
72/7 = 10 remainder 2

This means that Juan can build 10 full shelves (without any leftover lumber) using 18 feet of lumber. However, there will be 2 feet of leftover lumber.

Therefore, the maximum number of shelves Juan could build for a new bookcase using 18 feet of lumber is 10 shelves.