Question

What is the quotient($q$) and the remainder($r$) when -12 is divided by 5?

• A. $q=-3,r=3$
• B. $q=3,r=-3$
• C. $q=-2,r=-2$
• D. $q=-4,r=-8$

Answer 1

The correct option is A $q=-3,r=3$

Euclid’s division lemma states that for integers $a$ and $b,$ there exist unique integers $q$ and $r$ such that $a=bq+r,$ where $0\le r<|b|.$
Since $-12=5(-3)+3,$ we have quotient $q=-3,$ and remainder $r=3.$