Number Properties and Operations

ACT Math · Axiom Academy

LESSON Number Properties and Operations The rules that show up in the first 5-10 ACT Math questions — master them and each one takes 20-30 seconds 1. Order of Operations (PEMDAS) Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). Every expression on the ACT collapses in exactly this order — skip a step and you'll land on a real answer choice that's simply wrong. A second worked example — exponents before subtraction Solve 10-3^2+2 . Exponents go before subtraction/addition, so evaluate 3^2=9 first: 10-9+2 . Now work left to right: 10-9=1 , then 1+2=3 . Final answer: . Even numbers are (divisible by 2 with no remainder); odd numbers are . Six rules cover every combination the ACT will ask about — watch the checker below cycle through all six, live. If x is odd and y is even, is x+y even or odd? Mismatched parity under addition the sum is — no need to plug in actual numbers. 3. Primes, Factors, and Multiples A prime number has exactly two factors: 1 and itself ( ). Note that 2 is the only even prime — every other even number has 2 as a factor besides itself, so it can't be prime. 1 is not prime (it has only one factor, itself). Factors of 60 — every number that divides in evenly A factor tree breaks a number down into prime factors by repeatedly splitting it into two smaller factors, stopping only when every branch ends in a prime. Watch 60 build below. Factors vs. multiples — the direction matters

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