➗ 分数化简计算器（最简分数、带分数、循环小数）Simplify Fractions Calculator (Lowest Terms, Mixed Number, Repeating Decimal)
把分数化成最简分数：给出最大公约数、约分步骤、带分数、小数（循环小数用括号标出循环节）和百分数，分子分母可为负数。本地处理。Reduce a fraction to lowest terms with the greatest common divisor, the reduction step, the mixed number, the decimal (repeating digits shown in brackets) and the percentage. Negative numerators and denominators are allowed. Processed locally.
使用说明与常见问题How-to & FAQ
「分数化简计算器（最简分数、带分数、循环小数）」是什么？What is the Simplify Fractions Calculator (Lowest Terms, Mixed Number, Repeating Decimal) tool?
把分数化成最简分数：给出最大公约数、约分步骤、带分数、小数（循环小数用括号标出循环节）和百分数，分子分母可为负数。本地处理。Reduce a fraction to lowest terms with the greatest common divisor, the reduction step, the mixed number, the decimal (repeating digits shown in brackets) and the percentage. Negative numerators and denominators are allowed. Processed locally.
如何使用「分数化简计算器（最简分数、带分数、循环小数）」？How do I use the Simplify Fractions Calculator (Lowest Terms, Mixed Number, Repeating Decimal) tool?
在「分数化简计算器（最简分数、带分数、循环小数）」中，填写「分子」、「分母」等参数，结果会随输入实时计算并显示在下方。In the Simplify Fractions Calculator (Lowest Terms, Mixed Number, Repeating Decimal): Fill in "Numerator", "Denominator"; results are recalculated instantly as you type.
怎么化简分数？How do I simplify a fraction?
用分子和分母的最大公约数同时去除。例如 42/56：最大公约数是 14，42 ÷ 14 = 3，56 ÷ 14 = 4，所以 42/56 = 3/4。Divide the numerator and denominator by their greatest common divisor. For 42/56 the GCD is 14: 42 ÷ 14 = 3 and 56 ÷ 14 = 4, so 42/56 = 3/4.
括号里的数字是什么意思？What do the digits in brackets mean?
括号标出循环节：1/7 = 0.(142857) 表示 0.142857142857… 无限重复。Brackets mark the repeating block: 1/7 = 0.(142857) means 0.142857142857… repeating forever.
能举个计算实例吗？Can you show a worked example?
例如在「分数化简计算器（最简分数、带分数、循环小数）」中填 分子 = 42，分母 = -56，结果区显示：最简分数：−3/4；最大公约数：14；约分：42/−56 = −(42 ÷ 14)/(56 ÷ 14) = −3/4；带分数：−3/4；小数：−0.75；百分数：−75%For example, entering Numerator = 42, Denominator = -56 in the Simplify Fractions Calculator (Lowest Terms, Mixed Number, Repeating Decimal) gives: Lowest terms: −3/4; Greatest common divisor: 14; Reduction: 42/−56 = −(42 ÷ 14)/(56 ÷ 14) = −3/4; Mixed number: −3/4; Decimal: −0.75; Percent: −75%
哪些输入会被检查？Which inputs are validated?
「分数化简计算器（最简分数、带分数、循环小数）」会检查这些输入——「分子」：必须填写，须为不小于 -1,000,000,000,000且不大于 1,000,000,000,000的整数；「分母」：必须填写，须为不小于 -1,000,000,000,000且不大于 1,000,000,000,000的整数；绝对值超过 10¹⁵ 的数也会被拒绝。不符合时结果区显示具体提示，不会给出数字。The Simplify Fractions Calculator (Lowest Terms, Mixed Number, Repeating Decimal) checks its inputs — "Numerator": required, must be at least -1,000,000,000,000 and at most 1,000,000,000,000 (a whole number); "Denominator": required, must be at least -1,000,000,000,000 and at most 1,000,000,000,000 (a whole number); numbers above 10¹⁵ in absolute value are rejected too. When a value fails, the result area names the problem instead of showing a number.
有哪些选项可以调整？What options can I adjust?
「分数化简计算器（最简分数、带分数、循环小数）」的设置：「分子」默认 42；「分母」默认 -56。每次生成结果都按当前设置处理。Settings in the Simplify Fractions Calculator (Lowest Terms, Mixed Number, Repeating Decimal) — "Numerator" default 42; "Denominator" default -56. The result always uses the current settings.
计算精度如何？How precise are the results?
「分数化简计算器（最简分数、带分数、循环小数）」使用 JavaScript 双精度浮点数（约 15–16 位有效数字）；极大或极小的数值可能存在精度误差。The Simplify Fractions Calculator (Lowest Terms, Mixed Number, Repeating Decimal) uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.
「分数化简计算器（最简分数、带分数、循环小数）」免费吗？需要注册吗？Is the Simplify Fractions Calculator (Lowest Terms, Mixed Number, Repeating Decimal) free? Do I need an account?
「分数化简计算器（最简分数、带分数、循环小数）」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 Simplify Fractions Calculator (Lowest Terms, Mixed Number, Repeating Decimal) is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.