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 159 division 13, you may know off the top of your head that 13 multiplication 13 equals 169, 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, 12 multiplication 13 equals 156, which is three less than 159, so 159 division 13 equals 12 cap r times three.

Activity symbol 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?

Hint symbol

Discussion

We need to find how many groups of 20 are in 1500, so the calculation is:

20 times 1500

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.

Solution symbol

Answer

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:

multiline equation line 1 75 line 2 two times 150

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.

3.3.9 Equivalent Problems (Division Strategies)

3.3.11 Calculator Exploration—A Practical Problem