A ratio is the proportional relationship between two or more different quantities. A ratio is usually displayed using a colon ' : '.
Here is an example showing how ratios work. In a university, the ratio of professors to lecturers to students is $1:5:20$. This means for every $1$ professor there are $5$ lecturers and $20$ students.
If you want to convert ratios into fractions the following formula will help:
\begin{equation} \text{To convert the ratio A : B : C into fractions:} \frac{\text{A}}{\text{(A + B + C)}} , \frac{\text{B}}{\text{(A + B + C)}} , \frac {\text{C}}{\text{(A + B + C)}}. \end{equation}
You work as a psychologist. You often need to write prescriptions for patients. For patients with depression you administer Fluoxetine at a dose rate of $21$mg for every $60$kg of body weight per day. For patients with anxiety you administer Paroxetine at a dose rate of $15$mg for every $50$kg of body weight per day.
You have a patient who you have diagnosed with depression and anxiety. He weighs $91$kg; how much medication should you prescribe for a week?
Firstly, calculate how much of each drug he needs per day:
For Fluoxetine: he needs a dose rate of $21$mg per $60$kg and he weighs $91$kg. The method for calculating this is to divide $21$mg by $60$ to find out the dose rate per kg and then multiply this by $91$ to give:
$(21 \div 60) \times 91 = 31.85$mg of Fluoxetine per day.
For Paroxetine: he needs a dose rate of $15$mg per $50$kg and he weighs $91$kg. Divide $15$mg by $50$ to find the dose rate per kg and multiply by $91$ to give:
$(15\div 50) \times 91 = 27.3$mg of Paroxetine per day.
So per week you need to perscribe $31.85 \times 7 = 222.95$mg of Flouxetine and $27.3 \times 7 =191.10 $mg of Paroxetine to your patient.
Try our Numbas tests on background mathematics.