## Paint

## Opening

# Paint

Mia used the following reasoning to determine which paint is redder:

"I think it will be difficult to compare the two ratios in the problem because the numbers are so large. Maybe if I find equivalent ratios that have smaller numbers, it will be easier to solve the problem.

"The ratio of red to yellow in the Sunset paint is $\frac{24}{16}$. This ratio is equivalent to the ratio $\frac{3}{2}$.

"The ratio of red to yellow in the Apple paint is $\frac{48}{40}$. This ratio is equivalent to the ratio $\frac{6}{5}$.

"It’s easy to compare $\frac{3}{2}$ and $\frac{6}{5}$. I know that $\frac{3}{2}$ is greater than $\frac{6}{5}$. So, the Sunset paint is redder than the Apple paint."

- Talk to your partner about Mia's reasoning. Why is it more difficult to compare $\frac{24}{16}$ and $\frac{48}{40}$ than it is to compare $\frac{3}{2}$ and $\frac{6}{5}$?