I'm really struggling with division, could someone help?

W

whiteleaf

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So, I can do the actual working out of division itself pretty well. If I know the dividend and the divisor, then it's usually very easy to find the answer.

The problem arises with worded questions with no explicit calculation given. For some reason, I have a lot of trouble determining which number should be the dividend and which number should be the divisor.

For example, in the textbook I'm working from at the moment, one question was:

"A car uses 35 litres of petrol to travel 250 km. Assuming fuel consumption stays constant: a) Calculate how far to the nearest km the car can travel with 50 litres of petrol."​

I didn't know which way to work this out at all, but after giving up and looking at the answer, it makes a little bit of sense, but not completely.

Then I came across a question on inverse proportion:

"A journey takes two and a quarter hours when travelling at an average speed of 30mph. How long would the journey take when travelling at an average speed of 45 mph?"​

It's just not clear to me at all what numbers I have to divide, or even multiply, to reach the answer... and it's very frustrating and I'm really disappointed in myself that I can't think properly.

Can anyone provide a bit of advice?

Thanks

Whiteleaf
 
For these, it helps to know "distance equals rate times time". That directly helps with the first problem, and almost as much in the second, where one rate times time equals the other.
 
""A journey takes two and a quarter hours when travelling at an average speed of 30mph. How long would the journey take when travelling at an average speed of 45mph?"

You say it is a "question on inverse proprtion". How do you know that? Do you know what "inverse proportion" means?

You certainly be able to see that if you are traveling faster (45 mph is greater than 30 mph) then it will not take as long to go the same distance so the time required will be less than two and a quarter hours. That is, increasing the speed reduces the time. That is why it is "inverse". The length of time to go the same distance at 45 mph is \(\displaystyle \frac{30}{45}\) as much as at 30 mph. Note that the denominator is larger than the numerator so less than 1. \(\displaystyle \frac{30}{45}= \frac{2(15)}{3(15)}= \frac{2}{3}\). 2 and 1/4 hours is \(\displaystyle \frac{8}{4}+ \frac{1}{4}= \frac{9}{4}\) so the time is \(\displaystyle \frac{2}{3}\frac{9}{4}= \frac{3}{2}\). At this higher speed it will take 1 and a half hours rather than 2 and a quarter.
 
I would use ratios for the 1st problems

Think about this: If you use 5 liters to travel 30 km, then you would use 10 liters to go 60 km or 20 liters to go 120km.
Note that the ratio 30 km/5 liters = 60 km/10 liters = 120 km/10 liters = 12 km/liter

A car uses 35 litres of petrol to travel 250 km. Assuming fuel consumption stays constant: a) Calculate how far to the nearest km the car can travel with 50 litres of petrol .
Solution 250km/ 35 liters = x km/50 liters
 
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