Short Answer 
The product of two variables, **a** and **b**, decreases by **62.5%** after **a** is reduced by **25%** and **b** by **50%**. This results in the new product being **37.5%** of its original size.
Step 1: Understand the Reductions
To solve the problem, we first need to recognize that we are reducing two variables, a and b, by specific percentages. Specifically, a is reduced by 25% and b by 50%. This means:
- New value of a = 75% of a (or 0.75a)
- New value of b = 50% of b (or 0.5b)
Step 2: Calculate the New Size of the Product
Next, we determine the new size of the product ab after these reductions. We do this by multiplying the new values together:
- New product = (0.75a) * (0.5b) = 0.375ab
This tells us that the product ab has been reduced to 37.5% of its original size.
Step 3: Determine the Percentage Decrease
Finally, we calculate how much the product has decreased. Since the original product was 100%, and the new product is 37.5%, we can find the decrease:
- Decrease = 100% – 37.5% = 62.5%
This result shows that the overall decrease in the product ab is 62.5%.