What is 2/5 plus 8/13?
2/5 plus 8/13 equals 66/65 (or 1 1/65 as a mixed number) (or 1.015385 in decimal form). Learn the step-by-step solution to add 2/5 and 8/13 using Least Common Denominator and simplification.
Exact Answer
2/5 + 8/13 = 66/65
Simplified Fraction
66/65
Mixed Number
1 1/65
Decimal Value
1.015385
Percentage
101.5385%
Step-by-Step Solution: 2/5 + 8/13
Step 1
Find the Least Common Denominator (LCD)
The denominators 5 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 13 = 65.
LCD(5, 13) = 65
Step 2
Convert to Equivalent Fractions with Common Denominator 65
Multiply the numerator and denominator of 2/5 by 13, and multiply the numerator and denominator of 8/13 by 5 so both fractions share the common base 65.
2 × 13/5 × 13 = 26/65 and 8 × 5/13 × 5 = 40/65
Step 3
Add the Numerators
Now add the numerators (26 + 40 = 66) and keep the common denominator 65 unchanged.
26 + 40/65 = 66/65
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 66 and 65 is 1, confirming that 66/65 cannot be reduced further—it is already in its simplest irreducible form.
66/65
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (66) is greater than the denominator (65), divide 66 by 65: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/65.
66/65 = 11/65
Step 6
Decimal & Percentage Representation
Dividing the numerator 66 by denominator 65 produces a repeating decimal (approximately 1.015385, or 101.5385%).
66 ÷ 65 = 1.015385 (101.5385%)
Visual Representation
The diagram below illustrates 2/5 plus 8/13 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 66/65 |
| Mixed Number Form | 1 1/65 |
| Decimal Form | 1.015385 |
| Percentage | 101.5385% |
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Frequently Asked Questions
What is 2/5 plus 8/13 as a fraction?
2/5 + 8/13 in simplest fraction form is 66/65 (or 1 1/65 as a mixed number).
What is 2/5 plus 8/13 as a decimal?
2/5 + 8/13 converted to a decimal is 1.015385.
What is 2/5 plus 8/13 as a percentage?
2/5 + 8/13 expressed as a percentage is 101.5385%.
How do you write 2/5 plus 8/13 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 66/65 can be written as the mixed number 1 1/65.
Does 2/5 plus 8/13 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.015385...) because the denominator contains prime factors other than 2 and 5.