Addition-Subtraction Relationship

Arithmetic · Axiom Academy

LESSON Addition-Subtraction Relationship How addition and subtraction undo each other — and the fact families that connect them. 1. Addition Builds, Subtraction Undoes Start with 3 and add 2 to make 5 . Now take that same 2 back out: you land exactly where you started, at 3 . Subtracting the number you just added undoes it — that is what it means for the two operations to be inverses. Subtract the same 2 — back to 3 A fact family is a group of related facts built from the same three numbers. All four equations below use only 5 , 7 , and 12 . The whole (the sum) sits at the top of the triangle, and the two parts (the addends) sit at the bottom. Picture the parts as two bars. A bar of 5 and a bar of 7 join end to end into one bar of 12 — that is addition. Slide the 5 back off and a bar of 7 is left — that is subtraction. Same picture, run forward and then backward. 5 and 7 placed together span 12: 5 + 7 = 12 . Take the 5 away from the 12 and the 7 remains: 12 − 5 = 7 . The whole is the full 12-bar; the parts are the 5 and the 7 inside it. Addition assembles the whole from its parts; subtraction recovers one part by removing the other. Take any two different numbers — say 3 and 8 , which add to 11 . That one family delivers four facts : two additions and two subtractions. Learn any one of them and the other three come for free. Memorize 3 + 4 = 7 and you also know 4 + 3 = 7, 7 − 3 = 4, and 7 − 4 = 3. Is 15 − 8 = 7 right? Verify with the inverse: 7 + 8 = 15, so it checks out.

This is the written version of the interactive lesson above. See the full Arithmetic course.