Math 1 · Lesson 3 · Step One
Step One: Translate Subtraction and Division
Only addition and multiplication follow all the properties. So before you solve anything, you turn every subtraction into adding the opposite, and every division into multiplying by the inverse. Do that first, and most of the mistakes disappear.
About 30 minutes
Builds on Lesson 1 (inverse) and Lesson 2 (properties)
The parts of this lesson
Each part is its own short page. Go in order, or pick the one you need.
1Warm-up: rewrite before you computeTry these four on paper before reading on.Start here
2Why we only keep + and ×In Lesson 2 you tested the properties.
3The one move, in two placesSubtraction and division translate the exact same way.
4The sentence to say out loudChange the operation to its partner, and replace the number with its inverse.
5You will be multiplying fractionsBecause "divide by 2" becomes "multiply by 1 2 ," you need to multiply fractions comfortably.
6Negatives: think owe and haveOnce every subtraction is "add the opposite," you are only ever adding .
7The invisible 1sBecause 1 is the do-nothing number for multiplying, math lets it hide.
8Step One, every single timeBefore you solve, do two things: translate every subtraction to adding the opposite and every division to...
9Practice ProblemsTry them, get help one step at a time, then print how it went.
Printable study guide
One page of the method, worked examples, and a practice set with a full answer key. Print it, or work it on screen.
Where this goes next
Next lesson: Solving EquationsNow that everything is addition and multiplication, undo it: add the opposite to make a 0, multiply by the reciprocal to make a 1.
Unit Rates practiceEvery rate there is found by multiplying by a reciprocal to turn the time into 1. The same move you just learned.
Back to the Math 1 mapEvery Math 1 lesson, in course order.
Tell us what you thoughtA few quick questions about this lesson. It takes a minute, and it is how the lesson gets better.