Question

what is the ratio 175 to 250 written in fraction in LOWEST TERMS?

What is the ratio 16 to 40 written in fraction in LOWEST TERMS ?

Answer 1

For 175 : 250 divide them both by 25 to get $\frac{7}{10}$ < $\frac{175}{250}$
25 goes into 175 > 7 times > 25 into 250 is 10 times! > $\frac{7}{10}$
For the second one 16 : 40 just divide the top and bottom by 8 since 8 is a common factor of both which will give us $\frac{2}{5}$.
8 goes into 16, 2 times and 40, 5 times.

Answer 2

Well, factor each to find the GCF of the two numbers in a ratio, then divide by the GCF to simplify the fraction.

   175              250      
    /   \              /   \
  25  7           25  10
  / \                / \    / \  
 5 5              5 5  5 2

So the GCF of the two numbers in the ratio is 5 * 5 = 25.

(175/250) / (25/25) = 7/10

Now we do the same with 16 and 40:
 
     16              40
     /   \            /    \
   4     4       10     4
  /  \   / \       /  \    /  \
 2  2 2 2     5   2 2   2

GCF = 2 * 2 * 2 = 8

(16 / 40) / (8 / 8) = 2/5