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 \(\frac{4}{17}\).
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