The denominator of the fraction representing a rectangle divided into 4 parts is 4.
When discussing a rectangle divided into four parts, each part represents a fraction of the entire rectangle. Specifically, each part is one fourth of the rectangle. Hence, when we write this as a fraction, the number of parts the rectangle is divided into becomes the denominator. The fraction for one part of this rectangle is 1/4.
In fractions, when you multiply or divide, you work with the numerators (top numbers) and denominators (bottom numbers) respectively. If you were to work with a quantity like 4 yards as a fraction, you'd express it as 4 yd/1, effectively having a denominator of 1 which allows for easier multiplication or division with other fractions. If any units or numbers are the same in both the numerator and denominator, they can cancel each other out.
When calculating scale or proportions, such as finding missing dimensions using a scale factor, you set up a proportion like 1/4" : 4' = 8" : x. To solve for the unknown variable x, you would cross-multiply and divide accordingly.
In a rectangle divided into 4 parts, the total number of equal parts is represented by the denominator of a fraction. So, in this case, the denominator of the fraction representing the rectangle divided into 4 parts is 4.