[Verse 1]
When numbers collide in division's domain
Two integers dancing, let's break down their game
Take any whole number, call it "a" for short
And positive "b" that will serve as our port
[Chorus]
A equals b times q plus r, that's the magic spell
Quotient times divisor, remainder as well
Zero less than or equal, r stays below b
Division algorithm, sets integers free
A equals b times q plus r, memorize this line
Quotient and remainder, perfectly defined
[Verse 2]
Picture seventeen cookies, divided by five
How many full groups? Three complete and alive
Fifteen cookies sorted, two cookies remain
The leftover pieces that couldn't form chains
[Chorus]
A equals b times q plus r, that's the magic spell
Quotient times divisor, remainder as well
Zero less than or equal, r stays below b
Division algorithm, sets integers free
A equals b times q plus r, memorize this line
Quotient and remainder, perfectly defined
[Bridge]
Unique and certain, no guessing allowed
One quotient, one remainder, standing proud
The foundation stone for all math ahead
Without this truth, number theory's dead
[Verse 3]
Negative numbers? The rule still applies
Minus thirteen split by four, watch how it flies
Quotient negative four, remainder is three
The pattern persists through infinity
[Chorus]
A equals b times q plus r, that's the magic spell
Quotient times divisor, remainder as well
Zero less than or equal, r stays below b
Division algorithm, sets integers free
A equals b times q plus r, memorize this line
Quotient and remainder, perfectly defined
[Outro]
Every division tells this ancient tale
Quotient and remainder never fail
A equals b times q plus r
The algorithm that takes you far