Question

ella colored 320 of a rectangle green and another 25 of it red. she then divided the rest of the rectangle into several small rectangles. the area of each small rectangle was 140 of the area of the whole rectangle. part a write an expression that will determine the fraction of the rectangle divided into small rectangles. explain your answer in the space below. part b how many small rectangles were there?

Answer 1

`\( (9)/(20) \)` of the rectangle was divided into small rectangles. There were 18 small rectangles.

How to write an expression and find size?

To solve this problem, understand that the whole rectangle is divided into different fractions, with each fraction representing a part of the rectangle colored or divided in a certain way.

Part A

The expression to determine the fraction of the rectangle divided into small rectangles is:

`\[ 1 - \left( (3)/(20) + (2)/(5) \right) \]`

The total fraction colored is the sum of the green and red parts:

`\[ (3)/(20) + (2)/(5) = (3)/(20) + (8)/(20) = (11)/(20) \]`

Thus, the fraction for small rectangles is:

`\[ 1 - (11)/(20) = (9)/(20) \]`

This means
`\( (9)/(20) \)` of the rectangle is divided into small rectangles, which is equivalent to 0.45 or 45% of the whole rectangle.

Part B

The number of small rectangles is calculated by dividing the fraction of the area covered by small rectangles (
`\( (9)/(20) \)`) by the fraction that each small rectangle represents (
`\( (1)/(40) \)`).

Each small rectangle is
`\( (1)/(40) \)` of the whole rectangle. The number of such rectangles is:

`\[ ((9)/(20))/((1)/(40)) = (9)/(20) * (40)/(1) = 18 \]`

Therefore, there were 18 small rectangles.