➗ 随机分数生成器Random Fraction Generator

使用说明与常见问题How-to & FAQ

「随机分数生成器」是什么？What is the Random Fraction Generator tool?

批量生成随机分数，可设分母范围、真分数/假分数/带分数、是否约分、是否含负数，输出为 a/b、带分数或 LaTeX 格式，适合出数学练习题。Generate random fractions in bulk with a denominator range, proper/improper/mixed form, simplified or not, and optional negatives — output as a/b, mixed numbers or LaTeX for maths worksheets.

如何使用「随机分数生成器」？How do I use the Random Fraction Generator tool?

在「随机分数生成器」中，按需设置「数量」、「分母最小」、「分母最大」、「类型」、「最大值（假分数/带分数）」等选项，然后点击「生成」、「复制」按钮即可。In the Random Fraction Generator: Set "Count", "Min denominator", "Max denominator", "Type", "Max value (improper / mixed)", then click "Generate", "Copy".

真分数、假分数和带分数有什么区别？What are proper, improper and mixed fractions?

真分数的分子小于分母（如 3/4，小于 1）；假分数的分子大于或等于分母（如 7/3）；带分数把假分数写成整数加真分数（7/3 = 2 1/3）。生成时：假分数的值在 1 到“最大值”之间，约分后变成整数的（如 4/2）会跳过；带分数的整数部分在 1 到“最大值 − 1”之间等概率抽取，每个可能的结果出现的机会相同。勾选“不重复”时按数值判断，2/4 和 1/2 算同一个。A proper fraction has a numerator smaller than the denominator (3/4, less than 1). An improper fraction has a numerator at least as large (7/3). A mixed number writes an improper fraction as a whole number plus a proper fraction (7/3 = 2 1/3). Improper fractions are drawn between 1 and Max value, skipping any that simplify to a whole number (such as 4/2). For mixed numbers the whole part is drawn evenly from 1 to Max value − 1, so every possible result is equally likely. Unique compares values, so 2/4 and 1/2 count as the same.

约分后分母会小于设定范围吗？Can simplifying make the denominator smaller than the range?

会。例如分母 8 时抽到 4/8，约分后是 1/2。如果需要分母严格在范围内，请取消“自动约分”。Yes. With denominator 8 you might draw 4/8, which simplifies to 1/2. Untick Simplify if denominators must stay inside the range.

LaTeX 格式怎么用？How do I use the LaTeX output?

复制到 LaTeX 文档、Overleaf、Markdown 数学公式或支持 MathJax 的编辑器里，放在 $ … $ 之间即可显示为分数，例如 $\frac{3}{4}$。Paste it into a LaTeX document, Overleaf, Markdown math or any MathJax editor between $ … $ to render it as a fraction, e.g. $\frac{3}{4}$.

随机结果真的随机吗？Is the randomness truly random?

「随机分数生成器」使用浏览器的 crypto.getRandomValues（密码学安全随机数）生成结果，并做了无偏处理，每个结果出现的概率相同。The Random Fraction Generator uses crypto.getRandomValues (cryptographically secure randomness) with unbiased sampling, so every outcome is equally likely.

「随机分数生成器」免费吗？需要注册吗？Is the Random Fraction Generator free? Do I need an account?

「随机分数生成器」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Random Fraction Generator is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.