If the question is: if a product has an original price of $70, and there is a 12% discount on the product, what is the price of the product after the discount? then you are correct, you would take the original price of $70 and multiply by (1-.12), or .88.
You would only divide by 1.12 if the question asked for the price before taxes. Ie: The final price of a product, including taxes, was $70. What was the price before taxes were added? Then you would divide $70 by 1.12 and get $62.50. This is the same thing for markups, ie: if a product was marked up 12% and now costs $70, what was the price of the product before the markup? You would do the same thing, $70/1.12.
I was just giving an example if you had to solve for a tax rate. If you make a purchase of $100 and the tax rate is 10%, then you would pay $110.00 total. If you were only given the $110 after-tax amount and were told to determine the pre-tax amount at a tax rate of 10%, then you take $110/(1.1) to get back to the original $100. You are not doing this, you are given a price and calculating a discounted price based on a discount rate.