Triangle Perimeter with Fractions Calculator

Calculate the perimeter of a triangle when sides are given as fractions. Find LCD, add, and simplify.

Enter Three Sides as Fractions

Side a
/
Side b
/
Side c
/

Result

Perimeter
--
units

Step-by-Step Solution

Adding Fractions for Perimeter

When the sides of a triangle are given as fractions, finding the perimeter requires adding three fractions together. This involves finding a common denominator, converting each fraction, adding the numerators, and then simplifying the result.

Steps to Add Fractions

Step 1: Find the LCD

Find the Least Common Denominator of all three fractions.

LCD = LCM(d1, d2, d3)

Step 2: Convert Fractions

Rewrite each fraction with the LCD as the denominator.

a/b = (a × k)/(b × k)

Step 3: Add & Simplify

Add the numerators and simplify by dividing by the GCD.

P = (n1 + n2 + n3) / LCD

Example

Find the perimeter of a triangle with sides 1/2, 2/3, and 3/4.

  1. Find LCD of 2, 3, and 4: LCD = 12
  2. Convert: 1/2 = 6/12, 2/3 = 8/12, 3/4 = 9/12
  3. Add numerators: 6 + 8 + 9 = 23
  4. Result: 23/12 = 1 11/12 units

Tips for Working with Fractions

  • Always simplify fractions before starting to make the arithmetic easier.
  • If a side is a whole number, write it as a fraction with denominator 1.
  • Check that the result makes sense: the perimeter should be larger than any individual side.
  • Mixed numbers should be converted to improper fractions first.

Triangle Inequality with Fractions

Remember that the triangle inequality theorem must hold: the sum of any two sides must be greater than the third side. This applies regardless of whether the sides are expressed as fractions, decimals, or whole numbers. Our calculator verifies this condition and warns you if the sides cannot form a valid triangle.