3.3.10 Using a Related Problem
4. Solving an Easier, Related Problem and then Compensating
You can solve a problem where you already know the answer and adjust. For example, when solving , you may know off the top of your head that , and then you might reason that subtracting 13 from 169 is 156, the closest multiple of 13 to 169, without going over 159. In other words, , which is three less than 159, so .
Activity: Paper Supplies
A college bookstore buys pads of legal paper in bulk to sell to students in the law program at a cheap rate.
Each pack of paper contains 20 pads. If the store wants 1500 pads for the term, how many packs should be ordered?
We need to find how many groups of 20 are in 1500, so the calculation is:
If you imagine dividing some quantity of objects into 20 piles, one way to do it would be to divide it into ten piles instead, and then divide each of those piles in half. So, dividing a number by 20 is the same as dividing by ten, and then dividing the results by two.
Dividing 1500 by 10 gives 150. To divide 150 by 2, you can either split the problem up by dividing both 100 and 50 by two, and adding the results together to get 50 and 25, or you can write it out more formally like this:
Thus, the store should purchase 75 packs of paper. You might have used a slightly different approach to arrive at an answer—as long as your answer is correct, that’s okay!
There are lots of different strategies to help with division problems here, so don’t expect to feel comfortable with them all straight away. You might find it useful to start with to pick the first two and work on these. Good luck—and remember, if you find something that works well for you, it is fine to stick to that.