1. The problem asks why the fraction $\frac{10}{10}$ was used in the expression $\frac{2a}{3b}$ to find an equivalent fraction. 2. To find an equivalent fraction, we multiply the numerator and denominator by the same nonzero number. This number is often called a form of "1" because multiplying by it does not change the value of the fraction. 3. The fraction $\frac{10}{10}$ equals 1 because the numerator and denominator are the same, so multiplying by $\frac{10}{10}$ keeps the value unchanged. 4. Multiplying $\frac{2a}{3b}$ by $\frac{10}{10}$ gives: $$\frac{2a}{3b} \times \frac{10}{10} = \frac{2a \times 10}{3b \times 10} = \frac{20a}{30b}$$ 5. This new fraction $\frac{20a}{30b}$ is equivalent to the original $\frac{2a}{3b}$ because it represents the same value, just scaled up by a factor of 10. 6. In summary, $\frac{10}{10}$ is used because it is equal to 1 and multiplying by it changes the form but not the value of the fraction, allowing us to find an equivalent fraction.