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63 lines
2.1 KiB
Markdown
63 lines
2.1 KiB
Markdown
+++
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title = "Fractions and decimals"
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description = "Convert between fractions, terminating decimals, and repeating decimals; add, subtract, multiply, and divide rational numbers and mixed numbers."
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template = "chapter.html"
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weight = 10
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[extra]
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subject = "math"
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chapter_id = "rational-number-operations"
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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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Rational numbers can be written as fractions \(a/b\) with \(b\neq 0\). Decimals and mixed
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numbers are alternative forms of the same values.
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</p>
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<h2 id="convert" class="book-prose__heading">Converting fractions and decimals</h2>
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<ul>
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<li>Terminating decimal to fraction: \(0.375=\frac{375}{1000}=\frac{3}{8}\).</li>
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<li>Fraction to decimal: divide numerator by denominator.</li>
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<li>Repeating decimal to fraction: \(0.\overline{3}=\frac{1}{3}\).</li>
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</ul>
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<h2 id="add-subtract" class="book-prose__heading">Add and subtract fractions</h2>
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<p>
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Use a common denominator:
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</p>
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<p class="book-formula">
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\[
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\frac{2}{5}+\frac{1}{3}=\frac{6}{15}+\frac{5}{15}=\frac{11}{15}.
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\]
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</p>
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<h2 id="multiply-divide" class="book-prose__heading">Multiply and divide fractions</h2>
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<p>
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Multiply numerators and denominators. For division, multiply by the reciprocal.
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</p>
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<p class="book-formula">
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\[
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\frac{3}{4}\div\frac{5}{6}=\frac{3}{4}\times\frac{6}{5}=\frac{9}{10}.
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\]
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</p>
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<h2 id="mixed" class="book-prose__heading">Mixed numbers</h2>
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<p>
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Convert mixed numbers to improper fractions before operations.
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</p>
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<details class="book-question">
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<summary class="book-question__prompt">Checkpoint: simplify \(1\frac{1}{2}+2\frac{1}{3}\)</summary>
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<div class="book-question__solution">
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<p>\(\frac{3}{2}+\frac{7}{3}=\frac{9}{6}+\frac{14}{6}=\frac{23}{6}=3\frac{5}{6}\).</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: write \(0.125\) as a fraction</summary>
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<div class="book-question__solution">
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<p>\(0.125=\frac{125}{1000}=\frac{1}{8}\).</p>
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</div>
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</details>
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</div>
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