Question

1. the rectangle on the left is partitioned into

and
the rectangle on the right is partitioned into
. partition both rectangles so that they have the same number of equal parts. each rectangle was partitioned into
equal parts. each part is (\frac{1}{square}) of each rectangle.

Explanation:

Step1: Count the number of parts in each rectangle

The left - hand rectangle is partitioned into 5 equal parts (vertical partitions). The right - hand rectangle is partitioned into 4 equal parts (horizontal partitions).

Step2: Find the least common multiple of 4 and 5

The least common multiple of 4 and 5 is \(LCM(4,5)=20\).

Step3: Partition each rectangle into 20 equal parts

For the left - hand rectangle (originally in 5 parts), we divide each of the 5 parts into 4 sub - parts. So, \(5\times4 = 20\) parts.
For the right - hand rectangle (originally in 4 parts), we divide each of the 4 parts into 5 sub - parts. So, \(4\times5=20\) parts.

Answer:

The rectangle on the left is partitioned into fifths and the rectangle on the right is partitioned into fourths. Each rectangle was partitioned into 20 equal parts. Each part is \(\frac{1}{20}\) of each rectangle.