Mathematics

Adding Fractions Calculator

Add and subtract fractions with positive and negative numbers. Free online Adding Fractions Calculator for math — instant, accurate results, no signup needed.

a/b + c/d
5/6

Derivation

  1. ├── 01Givena = 1, b = 2, c = 1, d = 3
  2. ├── 02Formula{let t=e.a,a=e.b,n=e.c,r=e.d;const o=Gs(t × r+n × a,a × r),i=(0,l.A)(o,2),c=i[0],s=i[1];return"".concat(c," / ").concat(s)}
  3. ├── 03Substitute{let t=e.1,1=e.2,n=e.1,r=e.3;const o=Gs(t × r+n × 1,1 × r),i=(0,l.A)(o,2),1=i[0],s=i[1];return"".concat(1," / ").concat(s)}
  4. └── 04Compute a/b + c/d
Did you know?

Fractions in "numerator/denominator" notation date to India (Brahmagupta, c. 628 CE); Arabs introduced the horizontal bar around 1200.

§01What is

Understanding the Adding Fractions Calculator

The Adding Fractions Calculator computes a/b + c/d from 4 inputs: num 1, den 1, num 2, den 2. Add and subtract fractions with positive and negative numbers.

Mathematics shows up in every corner of daily life — budgeting, cooking, construction, engineering, even reading a bus schedule. A calculator like this lets you skip the scratch-paper step and move straight to the answer, without the arithmetic mistakes that creep in when the numbers get messy. The Adding Fractions Calculator sits in that toolkit — it add and subtract fractions with positive and negative numbers. Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.

§02The Formula

How it’s calculated

{let t=e.a,a=e.b,n=e.c,r=e.d;const o=Gs(t × r+n × a,a × r),i=(0,l.A)(o,2),c=i[0],s=i[1];return"".concat(c," / ").concat(s)}

Where

a
Num 1
b
Den 1
c
Num 2
d
Den 2
§03Practical Example

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: Num 1 = 1, Den 1 = 2, Num 2 = 1, Den 2 = 3.

  1. 01Start by noting the input — Num 1: 1.
  2. 02Start by noting the input — Den 1: 2.
  3. 03Start by noting the input — Num 2: 1.
  4. 04Start by noting the input — Den 2: 3.
  5. 05Substitute these values into the formula: {let t=e.a,a=e.b,n=e.c,r=e.d;const o=Gs(t × r+n × a,a × r),i=(0,l.A)(o,2),c=i[0],s=i[1];return"".concat(c," / ").concat(s)}
  6. 06Compute a/b + c/d: the calculator returns 5/6.
  7. 07Cross-check the answer by opening the Derivation panel above — every line of math is shown so you can follow the computation end-to-end.
§04FAQ

Frequently asked questions

Yes. The calculator implements the standard formula as documented and returns exact floating-point results. No approximations are used unless noted in the formula.
Your feedback

How useful was this calculator?

Your ratings stay in your browser — they help us learn which tools people actually rely on.

Rate it
Was this helpful?