The Correct Answer and Explanation is:
The correct simplified ratio of triangles to squares is 1:3.
For the sentence “For every 1 triangle there are [ 3 ] squares, therefore the simplified ratio of triangles to squares is 1:3.”
Explanation
A ratio is a way to compare the quantities of two different things. In this problem, we are asked to find the relationship between the number of triangles and the number of squares.
First, we need to count each shape in the image. By counting, we can see that there are 3 triangles and 9 squares. This gives us an initial, or unsimplified, ratio of 3 triangles to 9 squares, which is written as 3:9.
The next step is to simplify this ratio. Simplifying a ratio means finding the smallest whole numbers that represent the same relationship. To do this, we need to find the greatest common divisor, which is the largest number that can divide both parts of the ratio without leaving a remainder. For the numbers 3 and 9, the greatest common divisor is 3.
We then divide both numbers in the ratio by this common divisor:
- 3 (the number of triangles) divided by 3 equals 1.
- 9 (the number of squares) divided by 3 equals 3.
This gives us the simplified ratio of 1:3.
This simplified ratio tells us the most basic relationship between the two shapes. It means that for every one triangle, there are exactly three squares. You can see this visually in the image. The top triangle can be grouped with the top row of three squares, the middle triangle with the middle row, and the bottom triangle with the bottom row. Each of these groups demonstrates the 1:3 relationship. Therefore, the final simplified ratio of triangles to squares is 1:3.
