Integers

Division of Integers

Division of a negative integer by a positive integer

When we divide a negative integer by a positive integer, we divide them as whole numbers and then put a minus sign (–) before the quotient.

In general, for any two positive integers a and b, we have (–a) ÷ b = – (a ÷ b) where b ≠ 0.

Expression	Next step	Value
(–27) ÷ 3	= –(27 ÷ 3)	= –9
(–48) ÷ 8	= –(48 ÷ 8)	= –6
(–136) ÷ 4	= – (136 ÷ 4)	= –34
(–270) ÷ 9	= – (270 ÷ 9)	= –30

Division of a positive integer by a negative integer

When we divide a positive integer by a negative integer, we first divide them as whole numbers and then put a minus sign (–) before the quotient.

In general, for any two positive integers a and b, we have a ÷ (–b) = – (a ÷ b) where b ≠ 0.

Expression	Next step	Value
36 ÷ (–3)	= –(36 ÷ 3)	= –12
81 ÷ (–9)	= –(81 ÷ 9)	= –9
121 ÷ (–11)	= –(121 ÷ 11)	= –11
324 ÷ (–4)	= –(324 ÷ 4)	= –81

Division of a negative integer by a negative integer

When we divide a negative integer by a negative integer, we first divide them as whole numbers and then put a positive sign (+) before the quotient.

In general, for any two positive integers a and b, we have (– a) ÷ (–b) = a ÷ b where b ≠ 0.

Expression	Next step	Value
(–12) ÷ (– 6)	= + (12 ÷ 6)	= 2
(–112) ÷ (– 4)	= + (112 ÷ 4)	= 28
(–250) ÷ (– 5)	= + (250 ÷ 5)	= 50
(–1000) ÷ (– 10)	= + (1000 ÷ 10)	= 100