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83 lines
2.3 KiB
Markdown
83 lines
2.3 KiB
Markdown
+++
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title = "Integer arithmetic"
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description = "Multiply and divide integers from models to symbolic rules; apply order of operations with signed numbers in multi-step expressions."
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template = "chapter.html"
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weight = 9
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[extra]
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subject = "math"
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chapter_id = "integer-arithmetic"
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strand = "Number & Algebra"
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+++
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<div class="book-prose">
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<p>
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This chapter extends integer work to multiplication, division, and multi-step expressions.
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</p>
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<h2 id="sign-rules" class="book-prose__heading">Sign rules for multiplication and division</h2>
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<div class="book-table-wrap">
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<table class="book-table">
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<thead>
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<tr>
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<th scope="col">Operation</th>
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<th scope="col">Result sign</th>
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</tr>
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</thead>
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<tbody>
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<tr>
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<td>same signs</td>
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<td>positive</td>
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</tr>
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<tr>
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<td>different signs</td>
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<td>negative</td>
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</tr>
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</tbody>
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</table>
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</div>
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<p>
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Examples: \((-3)(-4)=12\), \(18\div(-3)=-6\).
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</p>
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<h2 id="patterns" class="book-prose__heading">Why negative times negative is positive</h2>
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<p>
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Arithmetic rules must stay consistent with distribution. This leads to
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\((-a)(-b)=ab\).
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</p>
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<h2 id="order" class="book-prose__heading">Order of operations with signed numbers</h2>
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<p>
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Use brackets, exponents, multiplication/division, then addition/subtraction.
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</p>
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<p class="book-formula">
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\(5-(-2)\times 3 = 5-(-6)=11\)
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</p>
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<h2 id="multi-step" class="book-prose__heading">Multi-step integer expressions</h2>
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<p>
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Keep signs with their numbers and rewrite subtraction as adding opposites when needed.
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</p>
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<details class="book-question">
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<summary class="book-question__prompt">Checkpoint: evaluate \((-6)\times 7\)</summary>
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<div class="book-question__solution">
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<p>\(-42\).</p>
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</div>
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</details>
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<details class="book-question">
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<summary class="book-question__prompt">Checkpoint: evaluate \(36\div(-9)\)</summary>
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<div class="book-question__solution">
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<p>\(-4\).</p>
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</div>
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</details>
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<details class="book-question">
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<summary class="book-question__prompt">Checkpoint: evaluate \(8-3(2-5)\)</summary>
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<div class="book-question__solution">
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<p>
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\(2-5=-3\), then \(8-3(-3)=8-(-9)=17\).
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</p>
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</div>
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</details>
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</div>
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