Add, subtract, multiply or divide fractions and simplify automatically
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Denominator cannot be 0
Fractions trip people up because the four operations each follow a different recipe. Addition and subtraction need a common denominator first; multiplication does not; division is multiplication in disguise. This calculator applies the right recipe for whichever operation you pick and hands back the answer in three useful forms: a fully simplified fraction, a decimal, and a mixed number.
Enter two fractions — numerator and denominator each, negatives allowed — and choose +, −, × or ÷. The result card shows the simplified fraction, the unsimplified intermediate (handy for checking homework working), the decimal value, the mixed-number form for improper results, and the common denominator used when adding or subtracting.
Every result is divided by the greatest common divisor of numerator and denominator, so 4/8 comes back as 1/2 and 6/4 as 3/2. A negative denominator is normalised onto the numerator, so 1/−2 is reported as −1/2.
1/2 + 1/3: cross-multiplying gives (1×3 + 1×2) / 6 = 5/6. As a decimal that is 0.833333. Now 3/4 ÷ 1/8: flip the second — 3/4 × 8/1 = 24/4 = 6. The mixed-number column shows 6 directly (integer results skip the fraction part).
| Operation | Working | Simplified |
|---|---|---|
| 1/2 + 1/3 | (3 + 2)/6 = 5/6 | 5/6 |
| 3/4 − 1/6 | (9 − 2)/12 = 7/12 | 7/12 |
| 2/3 × 3/5 | 6/15 | 2/5 |
| 3/4 ÷ 1/8 | (3×8)/(4×1) = 24/4 | 6 |
Recipes, woodworking plans and music timing are all written in fractions because halves and thirds describe reality exactly — 1/3 of a cup is not 0.33 of a cup. When a plan says 3/8 inch and you only have a 16ths ruler, the calculator's unsimplified intermediate (6/16) tells you instantly which mark to use. For denominators beyond 64 the decimal column is usually the more practical answer, and it is one row away.
分数容易出错，是因为四种运算各有一套做法：加减要先通分，乘法不用，除法本质是「反过来的乘法」。这个计算器会按你选的运算套用正确做法，并把答案同时给成三种形式：完全约分的分数、小数和带分数。
分别输入两个分数的分子与分母（允许负数），选择 +、−、× 或 ÷。结果卡会给出：约分后的分数、约分前的中间结果（方便对照作业步骤）、小数值、假分数结果对应的带分数，以及加减时实际使用的公分母。
每个结果都会除以分子分母的最大公约数：4/8 会变成 1/2，6/4 会变成 3/2。分母为负时符号会规范到分子上，1/−2 会显示为 −1/2。
1/2 + 1/3：交叉相乘得 (1×3 + 1×2) / 6 = 5/6，小数约 0.833333。再看 3/4 ÷ 1/8：翻转第二个分数——3/4 × 8/1 = 24/4 = 6。整数结果在带分数一栏直接显示 6，不带分数部分。
| 运算 | 过程 | 约分后 |
|---|---|---|
| 1/2 + 1/3 | (3 + 2)/6 = 5/6 | 5/6 |
| 3/4 − 1/6 | (9 − 2)/12 = 7/12 | 7/12 |
| 2/3 × 3/5 | 6/15 | 2/5 |
| 3/4 ÷ 1/8 | (3×8)/(4×1) = 24/4 | 6 |
菜谱、木工图纸和乐谱都用分数，因为二分之一、三分之一描述的是精确关系——三分之一杯并不等于 0.33 杯。当图纸上写着 3/8 英寸、而你的尺子只有 1/16 刻度时，计算器给出的约分前结果（6/16）能直接告诉你要读哪条刻度。分母大于 64 之后，小数一栏通常更实用，它就在旁边。
Cross-multiply: a/b + c/d = (a×d + c×b) / (b×d). For 1/2 + 1/3 that is (1×3 + 1×2) / 6 = 5/6. The calculator does this automatically and simplifies the result by the greatest common divisor.
Flip the second fraction and multiply: a/b ÷ c/d = a/b × d/c = (a×d)/(b×c). For 1/2 ÷ 1/4 that is (1×4)/(2×1) = 4/2 = 2.
Convert it first: 2 1/2 = 5/2 — multiply the whole number by the denominator, add the numerator, and keep the denominator. Enter 5 and 2. The Mixed Number stat shows the reverse conversion for results greater than 1.
Last reviewed: October 5, 2026 · How we calculate · Sources: Standard arithmetic
最近复核：2026 年 10 月 5 日 · 我们的计算方法 · 来源：标准算术法则