### Working out the dosage

##### Step 1: Developing the formula to be calculated

Claire requires 180mg of Paracetamol. The solution in the elixir contains 120mg of Paracetamol in 5mls of solution.

##### Step 2: Working out the fractions in the equation

Simplify the parts of the fraction to the smallest whole numbers. This makes the equation easier to work out. Remember that whatever you do to the top of the equation you must also do to the bottom of the equation.

Within this equation, you can divide 180 by 10, then 120 by 10, which leaves 18 over 12. Then you can simplify again by dividing the top and bottom by 6 which leaves 3 over 2, or:

180/120 divided by 10 = 18/12, divide again by 6 = 3/2

The final simplified equation can be easily calculated. 3 times 5 (the amount of solution) equals 15 over 2.

##### Step 3: Calculating how much medicine Claire requires

3/2 times (x) 5/1  = 15/2

15 divided by 2 equals 7 with 1 remaining. By extending beyond the decimal point and using a nought, 2 divides into 10 5 times. Therefore Claire needs 7.5mls of Paracetamol.