Question

Susan said, "I have four negative (blue) counters. If I double the number of counters and then share them equally with Sam, I'll have as many as I started with." Use integers to show why this is correct.

Answer 1

Susan initially has 4 blue counters.

If she doubles them, she will have twice that amount, or:

2*4 = 8 blue counters.

Now if she shares them equally with Sam, the total number of blue counters will be divided between the number of people in which the counters are being shared.

The counters are being shared between 2 people, then each one of them gets:

8/2 = 4 counters.

And in this way, Susan has the same number of counters that she had when she started.

Why does this happen?

Because at the start, she has an integer N and multiplies it by 2 to get 2*N

And then she divides that amount by 2

2*N/2 = N

So she is multipliying and dividing by the same number, so N does not change in the process.