Write this ratio as a fraction in simplest form without any units.
12 days to 6 weeks
The ratio of 12 days to 6 weeks can be written as:
$ \frac{12 \text{ days}}{6 \text{ weeks}} $
To simplify this ratio, we need to convert either days to weeks or weeks to days. Since there are 7 days in a week, we can convert weeks to days by multiplying by 7.
$ \frac{12 \text{ days}}{6 \text{ weeks}} = \frac{12 \text{ days}}{6 \times 7 \text{ days}} = \frac{12}{42} $
This fraction can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 6.
$ \frac{12}{42} = \frac{2 \times 6}{7 \times 6} = \frac{2}{7}$
Therefore, the ratio of 12 days to 6 weeks simplified to simplest form is $\frac{2}{7}$, without any units.
To convert the ratio from days to weeks, we need to make sure we're using the same unit. Since there are 7 days in a week, we can convert the 12 days to weeks by dividing it by 7:
12 days ÷ 7 = 1.714 weeks
Now, we can rewrite the ratio as:
1.714 weeks : 6 weeks
To simplify the ratio, we can divide both numbers by their greatest common divisor, which is 2:
1.714 ÷ 2 = 0.857
6 ÷ 2 = 3
So, the simplified ratio without any units is:
0.857 : 3