Dylan loved pencils. He had a whole box full of pencils in different colors and designs. One-seveth of them were yellow, one-sixth of them were blue, and the rest of the pencils had designs on them. What fraction represents the pencils with designs on them?
1/7 = 6/42
1/6 = 7/42
6/42 + 7/42 = 13/42
42/42 = 13/42 = 29/42
To find the fraction that represents the pencils with designs on them, we need to subtract the fractions that represent the yellow and blue pencils from 1 (since the sum of all the fractions should equal 1).
First, we need to find a common denominator for 1/7 and 1/6. The least common multiple of 7 and 6 is 42, so we can rewrite the fractions with a common denominator: 1/7 becomes 6/42, and 1/6 becomes 7/42.
Next, we add the fractions together: 6/42 + 7/42 = 13/42.
Finally, we subtract the sum from 1 to find the fraction that represents the pencils with designs on them: 1 - 13/42 = 42/42 - 13/42 = 29/42.
Therefore, the fraction that represents the pencils with designs on them is 29/42.