Question #22a8b

2 Answers
Jun 14, 2017

1:1 = 1/1 = 100% = 1.0 is correct.

Explanation:

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

Jun 24, 2017

This question points out how the ideas of ratios can be misleading.

The ratio 1 : 1 = 1/1 = 100% = 1.0 is correct, but it is easy to see how the other given answer came to be a consideration.

Explanation:

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?