A flag has a length of 3 1/3 feet when the width is 1 5/6 feet. Write the ratio of the length to the width as a fraction in simplest form.

length : width

= 3 1/3 : 1 5/6
= 10/3 : 11/6
= 20/6 : 11/6
= 20 : 11

To write the ratio of the length to the width, we need to divide the length by the width. Let's convert both measurements to improper fractions to make it easier.

The length, 3 1/3 feet, can be converted to an improper fraction:

3 1/3 = (3 * 3 + 1) / 3 = 10/3 feet

The width, 1 5/6 feet, can be converted to an improper fraction:

1 5/6 = (1 * 6 + 5) / 6 = 11/6 feet

Now, we can write the ratio of the length to the width:

(10/3) / (11/6)

To divide fractions, we invert the second fraction and multiply:

(10/3) * (6/11)

Now multiply the numerators and denominators:

(10 * 6) / (3 * 11) = 60/33

To simplify the fraction, we can find the greatest common divisor (GCD) of 60 and 33, which is 3. Therefore, we divide both the numerator and the denominator by 3:

60/33 = 20/11

So, the ratio of the length to the width is 20/11 in its simplest form.