Unit 1 Summary

Pre-Algebra · Axiom Academy

SUMMARY Unit 1: Foundations of Numbers A review of the building blocks of our number system — place value, the four operations, and the order they follow. Our number system is built on place value : the position of a digit decides how much it is worth. The system is base-10 — each place is worth ten times the place to its right. The four operations (addition, subtraction, multiplication, division) come in inverse pairs and obey consistent properties. When an expression mixes operations, order of operations (PEMDAS) tells you what to do first so everyone gets the same answer. Core Concept Place Value & Base-10 Our number system groups in tens. Each position is worth ten times the position to its right, so the position of a digit — not the digit itself — determines its value. Position determines value: the digit 5 means five tens in 52 but five ones in 25 . Periods & commas: digits are grouped into periods (ones, thousands, millions) separated by commas for easier reading. Core Concept The Four Operations Four basic ways to combine numbers. They pair up as inverses — each undoes the other. Addition: combining groups; regroup (carry) when a place tops 9 . Subtraction: the difference between groups; may require borrowing across places. Multiplication: repeated addition, or the area of a rectangular array. Division: splitting into equal groups — a quotient, plus a remainder when it does not divide evenly. Core Concept Properties & Relationships

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