## Managing fractions and decimals

What do you do if the Flow Rate calculation involves fractions such as ¼ of an hour or 0.5 litres? Find out how this is managed mathematically.

Our first problem is that we have an infusion running over 15 minutes and 50 mls of the infusion is being administered to the patient. We want to calculate the flow rate, and this answer needs to be in mls per hour.

Our formula for flow rate is volume divided by time, and we know the volume going into the patient, which is 50 mls of infusion, and we know that it is 15 minutes for the time. But if we keep going here, our answer will clearly be in mls per minutes and not mls per hour. We need to change the 15 minutes to hours and we do know that 15 minutes is quarter of an hour. So let’s put that in, even though it looks a little strange to have an fraction within a fraction.

What this is actually saying is how many quarters are in 50? Or what is 50 divided by one quarter? Now, you cannot cancel across a division sign and we cannot divide any numbers here. The next step is to turn the division sign into a multiplication sign, and flip the second fraction upside-down. So, as you see here, the problem turns into 50 times 4 because the second fraction - the quarter - gets turned upside-down. Now there is nothing we can cancel, but we can go ahead and just multiply.

Fifty times four is 200. That’s no surprise when you think about it, because there are four quarters in everyone and we have 50 of them. So 50, how many quarters, would be 50 times 4. And the mls unit is still on the top and the hours the denominator.

This time we have a similar problem, but the infusion this time is administered over 45 minutes. Once again, we need the formula flow rate equals volume over time. Once again the volume is 50 mls, and in this problem the time is 45 minutes. Once again, we need to change the minutes to hours. Similar to last time, we can change the 45 minutes to three quarters of an hour. This looks a little bit more complicated but we treat it the same way. It is really saying 50 mls divided by three-quarters of an hour. Like last time, we changed the division sign to times and flipped the second fraction. Three-quarters upside down is four-thirds, we can try to cancel if we can, but 3 does not divide nicely into 50, so we just multiply through.

50 multiplied by 4 makes 200, and then divide this by 3. It comes down to a decimal of 66.6 recurring, which can be rounded to 66.7 mls per hour, and if you want to round it to the nearest whole ml, than it will be 67 mls per hour. We have the same problem as we had in the first slide, where we have a 50 mil infusion running over 15 minutes again. Once again, we need to turn the 15 minutes into hours, but this time we will not use fractions, we’ll use a decimal. And 15 minutes is a quarter of an hour, and a quarter as a decimal is 0.25. Now, decimals within fractions do not work very well, but what you can do is turn that fraction into an equivalent fraction. That means a fraction that reduces down to the same thing, but the number inside it are proportionally bigger. We just need to use the numbers that are not complicated with a decimal points.

Here’s how we do it: if we jump that annoying decimal point to the right in the 0.25, it is okay as long as we increase the numerator in the same way, that is, we jump the decimal points in both numbers. That will give us 500 over 2.5, which is still difficult, so let’s move it another place to the right. And, what you do to the denominator you must do the same to the numerator. And that will give us 5000 over 25. This is equivalent, the numbers are bigger but the fraction overall comes down to the same thing that we started with. And most importantly, we are now dealing with only whole numbers within our fraction. So 5000 mls divided by 25 hours... This is straightforward long division, 5000 divided by 25 equals 200. And as we expected, the answer is 200 mls per hour.