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Lessons · Pharmacy · reducing and enlarging a formula

Reducing and enlarging a formula

A formula is scaled by one factor: the amount you want divided by the amount the formula makes, applied to every ingredient without exception.

Hone is a place to practise a career, one idea a day. This is one of its lessons, written out in full and free to read without an account.

What it is for

The formula in the book makes 500 g and the order is for 2 kg. Scaling is one multiplication done several times, and the mistake that ruins a batch is not the multiplication; it is the line somebody forgot to do it to.

How to think about it

Write the factor down once, on its own line, before touching an ingredient. Then go down the formula and multiply every line by it. Then add the scaled amounts up and check they come to the batch size you wanted.

Worked example

Formula makes 500 g; you want 2,000 g
Write both totals down first.
Factor = 2,000 / 500 = 4
One factor, for the whole formula.
An ingredient at 25 g x 4 = 100 g
Every line gets the same factor.
An ingredient at 5 g x 4 = 20 g
And the next, and the next.
The scaled lines add back to 2,000 g
If they do not, one line was missed.

Your turn

A formula makes 200 mL and you only need 50 mL. Write the factor.

50 / 200 = 

The trap

Scaling most of the lines and leaving one. The batch still looks right in the beaker and the strength is wrong, and the only place it shows is the check that the scaled lines add to the batch size.

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