Perimeter of a Triangle with Fractions Calculator
Calculate triangle perimeter with fractional sides including mixed numbers
Calculate Triangle Perimeter with Fractions
Current: 0 = 0.0000
Current: 0 = 0.0000
Current: 0 = 0.0000
Triangle Perimeter Results
Triangle Validity
Example Calculation
Triangle with Fractional Sides
Given: Triangle with sides a = 1/2, b = 1/3, c = 1/4
Step 1: Find common denominator (LCM of 2, 3, 4)
LCM calculation: 2 = 2¹, 3 = 3¹, 4 = 2² → LCM = 2² × 3¹ = 12
Step 2: Convert to common denominator:
• a = 1/2 = 6/12
• b = 1/3 = 4/12
• c = 1/4 = 3/12
Final Calculation
P = a + b + c
P = 6/12 + 4/12 + 3/12
P = (6 + 4 + 3)/12
P = 13/12 = 1 1/12
This matches the competitor's example exactly!
Fraction Input Guide
Mixed Numbers
Enter 2 1/5 as: Whole=2, Numerator=1, Denominator=5
Proper Fractions
Enter 3/4 as: Whole=0, Numerator=3, Denominator=4
Whole Numbers
Enter 5 as: Whole=5, Numerator=0, Denominator=1
Formula Reference
Basic Formula
P = a + b + c
Sum of all three sides
Mixed to Improper
a b/c = (a×c + b)/c
Convert mixed numbers
Common Denominator
LCM(d₁, d₂, d₃)
Find least common multiple
Triangle Inequality
a + b > c
Must hold for all combinations
Understanding Triangle Perimeter with Fractions
Working with Fractions
When triangle sides are expressed as fractions or mixed numbers, we need to add fractions properly. This involves finding a common denominator and converting all fractions before adding.
Types of Fractional Expressions
- •Proper fractions: 3/4, 1/2, 5/8 (numerator < denominator)
- •Improper fractions: 7/4, 9/2, 13/8 (numerator ≥ denominator)
- •Mixed numbers: 2 1/3, 1 3/4, 3 2/5 (whole + fraction)
Step-by-Step Process
1. Convert Mixed Numbers
Change mixed numbers to improper fractions
2. Find Common Denominator
Calculate LCM of all denominators
3. Convert Fractions
Express all fractions with common denominator
4. Add and Simplify
Sum numerators and simplify result
Why This Method Works
Consistent Units
Common denominator ensures same fractional units
Direct Addition
Can add numerators when denominators match
Exact Results
No rounding errors with fraction arithmetic