Let’s look at the ratio 6:36 first.
What do you notice about the two amounts: 6 and 36? Well, 36 is a multiple of 6, since 6•6 (or 6²) equals 36. So, we can reduce the ratio by a factor of 6.
However, let’s determine the percentage of lollipops to candy bars. To do so, we will convert the ratio into a fraction. Remember, fractions are a comparison of parts to a whole, where the whole is the total quantity of something and the numerator is the amount of parts. Therefore, we need to find the total amount of candy, meaning the sum of lollipops and candy bars in order to form a fraction. Thus, we’ll add the ratio quantities together, and that will provide the denominator of the fraction.
6+36=42
We want to see the percentage of lollipops to the total amount of candy, so we’ll use 6 as the numerator. This gives us the fraction:
6/42 = 14.285%
This percentage is important because if it matches the simplified ratio, we have a proportional relationship, which means we have an equivalent ratio. We have already determined that we can reduce the ratio by a factor of 6, so let’s do that:
6:36 ——> 6/6:36:6 ——> 1:6
The simplified ratio is 1:6, so there is 1 lollipop for every candy bar. Let’s make sure the percentage of this ratio shows an equivalent relationship with the original. So, we’ll convert this ratio into a fraction by the same process as the last one: add the two values together and that sum will be the denominator.
1+6=7
1 is the numerator:
1/7 = 14.285%
The percentages are equal, so the answer is: 1:6