Numo Integer Pro Mastery

Integer Rules & Properties — Quick Reference

Before you practice, skim these core integer rules. Numo the Fox turns every one of them into a mini-game below, so you can learn the rule and then play it until it sticks.

Compare Integers

• 5 > -2 — Greater or Less?: Numbers further right on the number line are bigger.
• |-5| = 5 — Absolute Value: The distance from zero. It is always positive.

Addition Rules & Properties

• -3 + (-4) = -7 — Same Signs: Add the numbers and keep the same sign.
• -5 + 2 = -3 — Different Signs: Subtract the smaller from the bigger, keep the sign of the bigger number.
• a + b = b + a — Commutative Property: You can add integers in any order.
• (a+b)+c = a+(b+c) — Associative Property: Grouping does not change the sum.
• a + 0 = a — Additive Identity: Adding zero changes nothing.
• a + (-a) = 0 — Additive Inverse: An integer plus its opposite equals zero.

Subtraction Rules & Properties

• a – b = a + (-b) — Keep-Change-Change: Change minus to plus, and flip the sign of the second number.
• a – b ≠ b – a — Not Commutative: Order matters in subtraction.

Multiplication Rules & Properties

• (-) × (-) = (+) — Same Signs: Two negatives (or two positives) multiplied give a positive answer.
• (+) × (-) = (-) — Different Signs: A positive times a negative gives a negative answer.
• a × 1 = a — Multiplicative Identity: Multiplying by 1 changes nothing.
• a × 0 = 0 — Zero Property: Anything multiplied by zero is zero.
• a×(b+c) = a×b + a×c — Distributive Property: Multiply across addition.

Division Rules & Properties

• (-) ÷ (-) = (+) — Same Signs: Dividing same signs gives a positive answer.
• (+) ÷ (-) = (-) — Different Signs: Dividing different signs gives a negative answer.
• a ÷ 1 = a — Division by 1: Any integer divided by 1 is itself.
• a ÷ 0 = Undefined — Division by Zero: Dividing by zero is undefined.