Division. Division with remainder

Division is the operation inverse to multiplication: when division is exact, if

a\div b=c

(and

b\neq 0

), then

c\cdot b=a

. In general you get a quotient

q

and remainder

r

such that

a=b\cdot q+r

with $0\le r<b$ . If

r=0

, we say

a

divides by

b

evenly. Terms:

a

— dividend,

b

— divisor,

q

— quotient,

r

— remainder. Check:

b\cdot q+r=a

; the remainder must be less than the divisor.

Link to multiplication:

a=bq \Rightarrow a\div b=q

(exact)

a=bq+r

0\le r<b

Remainder is smaller than divisor

Check:

b\cdot q+r=a

Visually: equal shares and a remainder

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