There is a difference between a ratio and a fraction even though students usually think there is none.
It is true that we can simplify a ratio the same way we simplify a fraction. For example, the ratio 6 to 9 or 6/9 is equivalent to the ratio 2 to 3 or 2/3. However, ratios do not always follow the same rules as fractions.
1. We do not add or subtract ratios although we can add or subtract fractions.
For instance, trying to add the following two ratios is just plain nonsense.
3 books / 8 pens and 6 books / 5 pens
2. A ratio does not always compare things that have the same units although a fraction compare things with the same units. With ratios, the units may or may not be the same.
For example, the fraction 8 cakes / 2 sodas does not make sense. Why not? It is because this will mean that we are trying to find out how many sodas can go into 8 cakes. Nonsense!
However, the ratio 8 cakes / 2 sodas make perfect sense even though the units are not the same. The ratio 8 cakes / 2 sodas just tells us that for every single soda, there are 4 cakes.
Similarly, the ratio 40 miles to 2 gallons or 20 miles to 1 gallon makes perfect sense if you are trying to see how far you can go with 1 gallon of gas.
The ratio 20 cakes / 15 cakes also makes perfect sense if you are comparing the number of cakes you made to the number of cakes your neighbor made in a given year.
3. The denominator in a fraction usually represents the number of parts in the same whole. For example, in the fraction 8 biscuits / 4, 4 represents the number parts in the same whole or 8 biscuits.
However, suppose a bag has 80 red balls and 50 blue balls. The ratio 80 / 50 can be simplified to 8 / 5. In the ratio 8 / 5, the denominator 5 represents the number of parts in another whole and that whole is the number of blue balls, not the number of red balls.