Mastering the Four Operations

Pre-Algebra · Axiom Academy

LESSON Mastering the Four Operations Addition, subtraction, multiplication, and division of whole numbers — each one shown as the regrouping mechanism that makes it work. 1. Addition with Regrouping (Carrying) When you add multi-digit numbers, sometimes the sum in one column is more than 9. That extra ten cannot stay in its column, so you carry it to the next column on the left. Watch the carried 1 ride up from the ones column to the tens column. 2. Subtraction with Regrouping (Borrowing) When you subtract, the top digit in a column is sometimes smaller than the bottom digit. You cannot subtract directly, so you borrow : take one ten from the next column to the left, which is worth ten ones here. Watch the 8 become a 7 as a ten moves over and turns the 2 into a 12 . 3. Multiplication Step by Step Multiplication is repeated addition. To multiply a two-digit number by a single digit, multiply each digit in turn — right to left — and carry whenever a product runs past 9, exactly as in addition. Watch each partial product drop into its place value below the line. Division splits a number into equal parts, working left to right . Long division is a four-step loop you repeat: divide , multiply , subtract , then bring down the next digit. Watch the loop run twice to finish . The four operations are linked in pairs. Understanding these links lets you check your work and see each operation as a shortcut for another. Watch each fact build, then run in reverse to undo itself.

This is the written version of the interactive lesson above. See the full Pre-Algebra course.