Ratio,Rate, Direct and Inverse Proportion

(Click here to read the glossary first)

Now that we have a through understanding of the 4 terms: Ratio,Rate, Direct and Inverse Proportion, I shall further elaborate on them.

Ratio and proportion are commonly used by us.We use it to solve mathematics problem sums. We use it to calculate whether the 230 grams of potato chips in NTUC Fairprice costing $2.30 is worth more than the 300 grams one in Cold Storage costing $2.70. In this case, the one in Cold Storage would be cheaper. This is illustrated in the explanation below:

NTUC Fairprice: 230g: $2.30 (Direct Proportion and Ratio)
Thus, 10g : $0.10

Hence, we know that for NTUC Fairprice, 10grams of chips cost $0.10.

Cold Storage: 300g: $2.70
Hence, 10g : S0.09

Thus, we know that for Cold Storage, 10grams of chips cost $0.09.

Finally, after calculating, we deduce that Cold Storage's potato chips are cheaper and buy theirs.

Furthermore, they are also utilized in industries like the automobile, traveling, medicine, shopping, stock trading and everyday activities, such as driving, babysitting, etc.

For example, when we are contemplating on buying either Car A or Car B, which are identical in all aspects except that they consume 100 litres of petrol per 100 kilometres traveled and 999 litres of petrol per 1000 kilometres traveled respectively.
By using ratio, rate and proportion in the diagram below:

Car A: 100l: 100km
Thus, 1l : 1km

Hence, we know Car A consumes 1 litre of petrol per kilometre or 1l/km

Car B: 999l: 1000km
Hence, 1l : 1 and 1/999km or approxiametely 1.001001001001001........

Thus, we know that Car B consumes 1 litre of petrol per 1.001001001001001...km or 1l/1.001001001001001...km.

Lastly, we find out that Car B travels 0.001001001001001...km per litre more than Car A and purchase it.

Another example of how Inverse proportion is used in our daily lives is when traveling from one place to another, be it to the supermarket, hotel, restaurant or bank. If we decide to arrive at our destination at a certain time, we will have to use Inverse proportion to find out how fast we should travel.

For example, Jim is going to the airport. His flight is at 7 p.m. He plans to set off for his journey at 4 p.m. at 40km/hr and the distance between the airport and his home is 120km. He falls asleep and wakes up at 6 p.m. Hurriedly, he rushes to the airport. However, he is unsure of whether to take a bus or a taxi which travel at 60km/hr and 120km/hr respectively.Help Jim find out which is the correct choice so he does not miss his flight.

At first:
We know that Jim has 3 hours to get to the airport---->4 p.m.---7 p.m.--->3 hours
We know that the distance he needs to travel in the 3 hours---->120km
Average speed per hour---> 120km/3hr---->40km/hr

Afterward:
We know that Jim has 1 hour to get to the airport---->6 p.m.---7 p.m.--->1 hour
Since 1 is 1/3 of 3, the time has been multiplied by a third, we must multiply the average speed by 3, which is the reciprocal of 1/3.
Average speed multiplied by 3---> 40km/hr X 3= 120km/hr.

Thus, Jim must take the taxi as he needs to travel 120km in 1 hour.


Common Misconceptions:
Often, people confuse Direct and Inverse proportion. Just remember that with direct proportion, both quantitative terms are changed by the same factor while with inverse proportion, they are changed by different factors.

Math Joke:
An infinite crowd of mathematicians enters a bar.
The first one orders a pint, the second one a half pint, the third one a quarter pint...
"I understand", says the bartender - and pours two pints.
(get it? Because n+ n/2+ n/4+ n/6+....where n stands for any positive number will never reach 2n.)

Thanks for reading my post!