This chapter extends integer work to multiplication, division, and multi-step expressions.

Sign rules for multiplication and division

Examples: \((-3)(-4)=12\), \(18\div(-3)=-6\).

Why negative times negative is positive

Arithmetic rules must stay consistent with distribution. This leads to \((-a)(-b)=ab\).

Order of operations with signed numbers

Use brackets, exponents, multiplication/division, then addition/subtraction.

\(5-(-2)\times 3 = 5-(-6)=11\)

Multi-step integer expressions

Keep signs with their numbers and rewrite subtraction as adding opposites when needed.

Checkpoint: evaluate \((-6)\times 7\)

\(-42\).

Checkpoint: evaluate \(36\div(-9)\)

\(-4\).

Checkpoint: evaluate \(8-3(2-5)\)

\(2-5=-3\), then \(8-3(-3)=8-(-9)=17\).