Question
There are 12 triangles and 20 circles. What is the simplest ratio of triangles to circles?

Question

Question There are 12 triangles and 20 circles. What is the simplest ratio of triangles to circles?

UpStudy AI · Accepted Answer

To find the simplest ratio of triangles to circles, we start with the numbers given: there are 12 triangles and 20 circles.

The ratio of triangles to circles can be expressed as:

$$
\text{Ratio} = \frac{\text{Number of triangles}}{\text{Number of circles}} = \frac{12}{20}
$$

Next, we simplify this fraction. We can do this by finding the greatest common divisor (GCD) of 12 and 20.

The factors of 12 are: 1, 2, 3, 4, 6, 12  
The factors of 20 are: 1, 2, 4, 5, 10, 20

The GCD of 12 and 20 is 4.

Now, we divide both the numerator and the denominator of the ratio by their GCD:

$$
\frac{12 \div 4}{20 \div 4} = \frac{3}{5}
$$

Thus, the simplest ratio of triangles to circles is:

$$
\boxed{3:5}
$$
The simplest ratio of triangles to circles is 3:5.

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