Sea Green Paint and the Ratio That Stays Put
Ines is painting a mural on the wall of the school gym, and she needs one exact shade of sea green. The recipe from her art teacher says to mix 3 cups of blue paint with 1 cup of yellow, and a ratio is a comparison of two amounts, so the ratio of blue to yellow in this recipe is 3 to 1.
The mural turns out to be bigger than Ines planned, so she needs a much larger batch, and she mixes 6 cups of blue with 2 cups of yellow. The batch is bigger, but the shade matches the first one perfectly. Doubling both amounts kept the ratio the same, because 6 to 2 is just 3 to 1 written with larger numbers, and ratios like these are called equivalent ratios.
Then her friend Tomas suggests a shortcut. "Let's add 2 more cups to each color," he says. Ines tries a small test with 5 cups of blue and 3 cups of yellow. The test looks much more yellow than the first batch. Adding the same amount to both parts changed the ratio to 5 to 3, and the color changed along with it.
The rule is simple. To keep a shade, multiply or divide both parts by the same number. Adding the same number to both parts creates a new ratio and a new shade. Painters, bakers, and cooks all depend on this idea every day.