Example

Subtracting 31-3 - 1 and 3(1)3 - (-1) with Counters

Using the two-color counter model, we can visualize subtracting integers when we do not initially have enough counters of the correct sign to take away. In these cases, we must first add neutral pairs (one positive and one negative counter, which sum to 0) until we have the required counters.

  • To compute 31-3 - 1, we start with 3 negative (red) counters. We need to subtract 1 positive (blue) counter, but we have none. We add one neutral pair, giving us 1 positive and 4 negative counters. We then take away the 1 positive counter, leaving 4 negative counters. Thus, 31=4-3 - 1 = -4.
  • To compute 3(1)3 - (-1), we start with 3 positive (blue) counters. We need to subtract 1 negative (red) counter, but we have none. We add one neutral pair, giving us 4 positive and 1 negative counters. We then take away the 1 negative counter, leaving 4 positive counters. Thus, 3(1)=43 - (-1) = 4.

Adding neutral pairs effectively converts the subtraction problem into adding the opposite without changing the overall value.

0

1

Updated 2026-05-01

Contributors are:

Who are from:

Tags

OpenStax

Intermediate Algebra @ OpenStax

Ch.1 Foundations - Intermediate Algebra @ OpenStax

Algebra

Related