What is 2/27 plus 3/13?
2/27 plus 3/13 equals 107/351 (or 0.304843 in decimal form). Learn the step-by-step solution to add 2/27 and 3/13 using Least Common Denominator and simplification.
Exact Answer
2/27 + 3/13 = 107/351
Simplified Fraction
107/351
Mixed Number
Proper (107/351)
Decimal Value
0.304843
Percentage
30.4843%
Step-by-Step Solution: 2/27 + 3/13
Step 1
Find the Least Common Denominator (LCD)
The denominators 27 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 27 × 13 = 351.
LCD(27, 13) = 351
Step 2
Convert to Equivalent Fractions with Common Denominator 351
Multiply the numerator and denominator of 2/27 by 13, and multiply the numerator and denominator of 3/13 by 27 so both fractions share the common base 351.
2 × 13/27 × 13 = 26/351 and 3 × 27/13 × 27 = 81/351
Step 3
Add the Numerators
Now add the numerators (26 + 81 = 107) and keep the common denominator 351 unchanged.
26 + 81/351 = 107/351
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 107 and 351 is 1, confirming that 107/351 cannot be reduced further—it is already in its simplest irreducible form.
107/351
Step 5
Decimal & Percentage Representation
Dividing the numerator 107 by denominator 351 produces a repeating decimal (approximately 0.304843, or 30.4843%).
107 ÷ 351 = 0.304843 (30.4843%)
Visual Representation
The diagram below illustrates 2/27 plus 3/13 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 107/351 |
| Mixed Number Form | 107/351 |
| Decimal Form | 0.304843 |
| Percentage | 30.4843% |
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Frequently Asked Questions
What is 2/27 plus 3/13 as a fraction?
2/27 + 3/13 in simplest fraction form is 107/351.
What is 2/27 plus 3/13 as a decimal?
2/27 + 3/13 converted to a decimal is 0.304843.
What is 2/27 plus 3/13 as a percentage?
2/27 + 3/13 expressed as a percentage is 30.4843%.
Does 2/27 plus 3/13 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 0.304843...) because the denominator contains prime factors other than 2 and 5.