Math 1 · Lesson 1 · Identity and inverse · part 2 of 6
The parallel: adding and multiplying
Say the math word first, then the plain English, every time.
The parallel: adding and multiplying
Say the math word first, then the plain English, every time.
Adding
Additive identity = the do-nothing number for adding. Add it and the number keeps its identity. a + 0 = a
Additive inverse = the opposite, the undo partner for adding. It brings you back to 0. a + (-a) = 0
Multiplying
Multiplicative identity = the do-nothing number for multiplying. Multiply by it and the number stays itself. a x 1 = a
Multiplicative inverse = the reciprocal, the undo partner for multiplying. It brings you back to 1. a x 1a = 1
| Term | Symbols | Plain English |
|---|---|---|
| Identity property | a + 0 = a and a x 1 = a | Adding 0 or multiplying by 1 never changes a number. Ever. |
| Inverse property | a + (-a) = 0 and a x 1a = 1 | Every number has an undo partner that brings it back to the do-nothing number. (Except 0 has no reciprocal.) |
Quick ones: the opposite of 6 is -6, of -2.5 is 2.5, of 12 is -12. The reciprocal of 6 is 16, of 25 is 52, of -4 is -14 (the sign stays, because -4 x (-14) = +1), and of 1 is 1.
Three quick questions
Which number is its own opposite? 0. Which numbers are their own reciprocal? 1 and -1. Why does 0 have no reciprocal? Nothing times 0 makes 1.