If there are 12 doctors and 42 nurses, what is the ratio of doctors to nurses reduced to lowest terms?

2:7

Step-by-step explanation:

Ratio of doctors to nurses is 12:42

Reduce to lowest terms means you have to find a number that 12 and 42 can be divided by

Both numbers are divisible by 3

12/3 = 4

42/3=14

4:14

Both numbers can still be reduced and are divisible by 2

4/2=2

14/2=7

2:7

7 cannot be reduced any more.

The lowest term is 2:7

Answer: 2/7

Step-by-step explanation: We can write a ratio using the word to, using a colon, or using a fraction bar. Here, since we want our answer in lowest terms, I would write the ratio using a fraction bar.

So we need to compare the number of doctors

to the number of nurses.

We know that there are 12 doctors so we write 12 in the numerator of our ratio and we also know there are 42 nurses so we write 42 in the denominator of our ratio and this gives us 12/42.

Notice however that 12/42 is not in lowest terms so we need to divide the numerator and the denominator

by their greatest common factor of 6 to get 2/7.

So the ratio of the number of doctors to the number of nurses is 2/7.