How do you simplify to tell whether the ratios #3/10, 9/20# form a proportion?

A proportion, by definition, means that two ratios are equal.

To check if two ratios are equal, you have to bring both to their simplest form and see if you get the same value.

Let's look at the two ratios we have and see if we can simplify them.

#3/10# cannot be simplified any further because #3# and #10# do not have any common factors. #9/20# also cannot be simplified any further for the same reason - this means that the two ratios we had are already in simplest form.

Therefore, #3/10# and #9/20# do not form a proportion because #3/10# does not #=# #9/20#

#3/10# and #6/20# would have formed a proportion though because we can simplify #6/20# by dividing the numerator and denominator by the common factor of #2# to get #3/10#.

Probably the quickest check is to cross-multiply.

If the fractions are equivalent, their cross-products are equal.

# 3/10 and 9/20#

#3xx 20 !=10xx9#
#" "60!=90#

So the ratios do not form a proportion.

Another check is to divide each fraction to get a decimal, these are easy to compare.

#3/10 = 0.3" "and" "9/20 = 0.45#
They are not equal.

Changing to a common denominator is another option:

#3/10 xx 2/2 = 6/20#

#6/20 != 9/20#