Write each ratio in simplest form.

1. 50 m : 30 m

First, we can tell that both these numbers have the same unit (m), so we don't need to convert anything.

Second, both these numbers are divisible by 10.  50m/10 : 30m/10  =  5m : 3m

5m : 3m is the simplest ratio.

2. 6 ft to 6 yds  (can be written as 6ft : 6yd)

First, we need to convert ft to yds in order to have the same unit. We know that 3ft = 1yd, so divide 6 by 3 and you get 2yds. 

Now the ratio is 2yd : 6yd.

Second, both these numbers are divisible by 2.  2yd/2 : 6yd/2  =  1yd : 3yd

3. 120 ft / 13.36 cm  (can be written as 120ft : 13.36cm

First, we realize we need to convert to make the units the same. There are 30.48 cm in 1 ft. 30.48 cm x 120 = 3657.6cm

Now the ratio is 3657.6cm : 13.36cm

Also.....

50 m : 30 m   \(=\frac{50\,\text{m}}{30\,\text{m}}=\frac{5\,\text m}{3\,\text m}=\frac53=\)   5 : 3

6 ft  to  6 yd   \(=\frac{6\text{ ft}}{6\text{ yd}}=\frac{1\text{ ft}}{1\text{ yd}}=\frac{1\text{ ft}}{3\text{ ft}}=\frac13=\)   1  to  3

\(\frac{120\text{ ft}}{13.36\text{ cm}}=\frac{120\text{ ft}\cdot\frac{1\text{ ft}}{1\text{ ft}}}{13.36\text{ cm}} =\frac{120\text{ ft}\cdot\frac{30.48\text{ cm}}{1\text{ ft}}}{13.36\text{ cm}} =\frac{3657.6\text{ cm}}{13.36\text{ cm}}=\frac{3657.6}{13.36}=\frac{100}{100}\cdot\frac{3657.6}{13.36}= \frac{365760}{1336}=\frac{45720}{167}\)