What is 2/13 plus 5/13?
2/13 plus 5/13 equals 7/13 (or 0.538462 in decimal form). Learn the step-by-step solution to add 2/13 and 5/13 using Least Common Denominator and simplification.
Exact Answer
2/13 + 5/13 = 7/13
Simplified Fraction
7/13
Mixed Number
Proper (7/13)
Decimal Value
0.538462
Percentage
53.8462%
Step-by-Step Solution: 2/13 + 5/13
Step 1
Check the Denominators (Like Fractions)
Both fractions already share the identical denominator (13). Because these are like fractions, no conversion to a common denominator is required—we directly add their numerators while keeping the denominator 13.
2/13 + 5/13
Step 2
Add the Numerators
Now add the numerators (2 + 5 = 7) and keep the common denominator 13 unchanged.
2 + 5/13 = 7/13
Step 3
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 7 and 13 is 1, confirming that 7/13 cannot be reduced further—it is already in its simplest irreducible form.
7/13
Step 4
Decimal & Percentage Representation
Dividing the numerator 7 by denominator 13 produces a repeating decimal (approximately 0.538462, or 53.8462%).
7 ÷ 13 = 0.538462 (53.8462%)
Visual Representation
The diagram below illustrates 2/13 plus 5/13 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 7/13 |
| Mixed Number Form | 7/13 |
| Decimal Form | 0.538462 |
| Percentage | 53.8462% |
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Frequently Asked Questions
What is 2/13 plus 5/13 as a fraction?
2/13 + 5/13 in simplest fraction form is 7/13.
What is 2/13 plus 5/13 as a decimal?
2/13 + 5/13 converted to a decimal is 0.538462.
What is 2/13 plus 5/13 as a percentage?
2/13 + 5/13 expressed as a percentage is 53.8462%.
Does 2/13 plus 5/13 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 0.538462...) because the denominator contains prime factors other than 2 and 5.