Fraction of color of tiles

Question

The tile backsplash will be a mixture of colors of 3-inch square tiles. 2/5 of the tiles will be red, 1/6 will be blue, 3/10 will be green, and the rest will be yellow. What fraction of the tiles will be yellow?

Answer 1

To determine the fraction of tiles that remain, need to put existing tile fractions over a common denominator, which is 30.

red: 2/5 = 12/30 (multiply top and bottom by 6)

blue: 1/6 = 5/30 (multiply top and bottom by 5)

green: 3/10 = 9/30 (multiply top and bottom by 3)

Adding together

12/30+5/30+9/30 = 26/30. 30/30-26/30 = 4/30. The remaining 4/30 would be yellow.

This reduces to 2/15 yellow.