2.3 KiB
+++ title = "Integer arithmetic" description = "Multiply and divide integers from models to symbolic rules; apply order of operations with signed numbers in multi-step expressions." template = "chapter.html" weight = 9 [extra] subject = "math" chapter_id = "integer-arithmetic" strand = "Number & Algebra" +++
This chapter extends integer work to multiplication, division, and multi-step expressions.
Sign rules for multiplication and division
| Operation | Result sign |
|---|---|
| same signs | positive |
| different signs | negative |
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 \(8-3(-3)=8-(-9)=17\).