Question

A pattern has 16 blue triangles to every 52 yellow triangles. What is
the ratio of blue triangles to all triangles?

Answer 1

To find the ratio of blue triangles to all triangles, we first need to determine the total number of triangles. We have:

- 16 blue triangles
- 52 yellow triangles

Now, let's calculate the total number of triangles:

\[
\text{Total triangles} = \text{Blue triangles} + \text{Yellow triangles} = 16 + 52 = 68
\]

Next, we can find the ratio of blue triangles to the total number of triangles:

\[
\text{Ratio of blue triangles to all triangles} = \frac{\text{Blue triangles}}{\text{Total triangles}} = \frac{16}{68}
\]

To simplify this ratio, we can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 16 and 68 is 4.

Dividing both by 4:

\[
\frac{16 \div 4}{68 \div 4} = \frac{4}{17}
\]

Thus, the ratio of blue triangles to all triangles is \(\frac{4}{17}\).