Question #22a8b

A 1:1 ratio can be written as #1/1#.
#1/1# does not equal #1/2#.

However, #1/1=2/2#.

You are correct when you say 1:1 = #1/1# = 100% = 1.0

The ratio #1:1# simply states that for every one of something there is also one of something else. If the ratio is #1:1# then:

For every #5600# birds there are #5600# bees.
For every #30# students there were #30# parents at the meet.
For every dog there is a cat.

To extrapolate from the above, it means for every #10,000# dogs there are #10,000# cats. The ratio is still #1:1#.

But now someone wants to know how many animals are dogs if there are #72,080# animals in a #1:1# ratio.
Looking at the above examples where all values are equal to each other, it makes sense to simply divide the #72,080# by #2# or: #1/2xx(72,080)# to arrive at the correct answer of #36,040# dogs.
And there is the #1/2 = 50% = 0.5# as shown in the question.

When working with ratios what we are really doing is summing the terms of the ratio then dividing the total quantity by each term over the sum.

So for a #1:1# ratio the sum is #1+1=2# and we arrive at:

#1/2xx72,080= 36,040# dogs plus #1/2xx72,080= 36,040# cats.

Now we can try the situation where the ratio is changed to #3:5# dogs to cats with the total quantity of animals still at #72,080.#

For a #3:5# ratio the sum is #3+5=8# and we arrive at:

#3/8xx72,080= 27,030# dogs plus #5/8xx72,080= 45,050# cats.

Does anybody want a cat?