Finding the original amount

Is this correct?  The cost of a train ticket from Manchester to London has risen by 25% to £109. Find the original cost of the ticket.  25% of £109 is £27.25  £109 - £27.25 = £81.75  So the original price is £81.75 ???

How can we check our answer?  If we increase £81.75 by 25% we should get £109. Do we?  25% of £81.75 = £ (round to £20.44)  Adding this to £81.75 gives £  What has gone wrong???

To get the correct answer use multipliers!  The original price of the train ticket has been increased by 25%  What is the multiplier to increase by 25%  Original price x 1.25 = £109 (new price)  We need to work backwards to find the original price  The opposite of multiplying by 1.25 is dividing by 1.25  So the original price is £109 ÷ 1.25 = £87.20

Reductions…  The price of a shirt has been reduced in a sale by 12.5% to £21. What did it originally cost?  The multiplier to reduce by 12.5% is  Original price x = £21 (sale price)  Working backwards, the opposite of multiplying by is dividing by  So the original price was £21 ÷ = £24