Why is 3 – 5 = 3 + (-5)?

By William McCallum

You will never have to subtract again.

Students sometimes learn about addition and subtraction of integers using integer chips. These are circular chips, with a yellow chip representing +1 and a red chip representing -1. You start with the all-important rule that

1+(1)=0



, so you can add or remove a red-yellow pair without changing the number. To calculate the right hand side of the equation in the title,

3+(5)



, you put 3 yellow chips together with 5 red chips, then remove 3 red-yellow pairs, leaving 2 red chips. So

3+(5)=2



.

Continue reading “Why is 3 – 5 = 3 + (-5)?”

Up ↑