openfreebooks-bookgenerator/content/math/rational-number-operations/core.html

<div class="book-prose">
  <p>
    Rational numbers can be written as fractions \(a/b\) with \(b\neq 0\). Decimals and mixed
    numbers are alternative forms of the same values.
  </p>

  <h2 id="convert" class="book-prose__heading">Converting fractions and decimals</h2>
  <ul>
    <li>Terminating decimal to fraction: \(0.375=\frac{375}{1000}=\frac{3}{8}\).</li>
    <li>Fraction to decimal: divide numerator by denominator.</li>
    <li>Repeating decimal to fraction: \(0.\overline{3}=\frac{1}{3}\).</li>
  </ul>

  <h2 id="add-subtract" class="book-prose__heading">Add and subtract fractions</h2>
  <p>
    Use a common denominator:
  </p>
  <p class="book-formula">
    \[
    \frac{2}{5}+\frac{1}{3}=\frac{6}{15}+\frac{5}{15}=\frac{11}{15}.
    \]
  </p>

  <h2 id="multiply-divide" class="book-prose__heading">Multiply and divide fractions</h2>
  <p>
    Multiply numerators and denominators. For division, multiply by the reciprocal.
  </p>
  <p class="book-formula">
    \[
    \frac{3}{4}\div\frac{5}{6}=\frac{3}{4}\times\frac{6}{5}=\frac{9}{10}.
    \]
  </p>

  <h2 id="mixed" class="book-prose__heading">Mixed numbers</h2>
  <p>
    Convert mixed numbers to improper fractions before operations.
  </p>

  <details class="book-question">
    <summary class="book-question__prompt">Checkpoint: simplify \(1\frac{1}{2}+2\frac{1}{3}\)</summary>
    <div class="book-question__solution">
      <p>\(\frac{3}{2}+\frac{7}{3}=\frac{9}{6}+\frac{14}{6}=\frac{23}{6}=3\frac{5}{6}\).</p>
    </div>
  </details>

  <details class="book-question">
    <summary class="book-question__prompt">Checkpoint: write \(0.125\) as a fraction</summary>
    <div class="book-question__solution">
      <p>\(0.125=\frac{125}{1000}=\frac{1}{8}\).</p>
    </div>
  </details>
</div>