+++
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"
+++

<div class="book-prose">
  <p>
    This chapter extends integer work to multiplication, division, and multi-step expressions.
  </p>

  <h2 id="sign-rules" class="book-prose__heading">Sign rules for multiplication and division</h2>
  <div class="book-table-wrap">
    <table class="book-table">
      <thead>
        <tr>
          <th scope="col">Operation</th>
          <th scope="col">Result sign</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <td>same signs</td>
          <td>positive</td>
        </tr>
        <tr>
          <td>different signs</td>
          <td>negative</td>
        </tr>
      </tbody>
    </table>
  </div>
  <p>
    Examples: \((-3)(-4)=12\), \(18\div(-3)=-6\).
  </p>

  <h2 id="patterns" class="book-prose__heading">Why negative times negative is positive</h2>
  <p>
    Arithmetic rules must stay consistent with distribution. This leads to
    \((-a)(-b)=ab\).
  </p>

  <h2 id="order" class="book-prose__heading">Order of operations with signed numbers</h2>
  <p>
    Use brackets, exponents, multiplication/division, then addition/subtraction.
  </p>
  <p class="book-formula">
    \(5-(-2)\times 3 = 5-(-6)=11\)
  </p>

  <h2 id="multi-step" class="book-prose__heading">Multi-step integer expressions</h2>
  <p>
    Keep signs with their numbers and rewrite subtraction as adding opposites when needed.
  </p>

  <details class="book-question">
    <summary class="book-question__prompt">Checkpoint: evaluate \((-6)\times 7\)</summary>
    <div class="book-question__solution">
      <p>\(-42\).</p>
    </div>
  </details>

  <details class="book-question">
    <summary class="book-question__prompt">Checkpoint: evaluate \(36\div(-9)\)</summary>
    <div class="book-question__solution">
      <p>\(-4\).</p>
    </div>
  </details>

  <details class="book-question">
    <summary class="book-question__prompt">Checkpoint: evaluate \(8-3(2-5)\)</summary>
    <div class="book-question__solution">
      <p>
        \(2-5=-3\), then \(8-3(-3)=8-(-9)=17\).
      </p>
    </div>
  </details>
</div>