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 } { } \\) of each rectangle.

Explanation:

Step1: Count the initial partitions

The left rectangle is partitioned vertically. Counting the vertical parts, we see it is partitioned into fifths (since there are 5 vertical columns). The right rectangle is partitioned horizontally. Counting the horizontal parts, we see it is partitioned into thirds (since there are 3 horizontal rows).

Step2: Find a common number of parts

We need to find a common multiple of 5 and 3. The least common multiple of 5 and 3 is \(5\times3 = 15\).

Step3: Re - partition the rectangles

For the left rectangle (originally in fifths), to get 15 parts, we divide each of the 5 fifths into 3 smaller parts. For the right rectangle (originally in thirds), we divide each of the 3 thirds into 5 smaller parts.

Answer:

The rectangle on the left is partitioned into fifths and the rectangle on the right is partitioned into thirds. Each rectangle was partitioned into 15 equal parts. Each part is \(\frac{1}{15}\) of each rectangle.