What is 2/6 plus 9/13?
2/6 plus 9/13 equals 40/39 (or 1 1/39 as a mixed number) (or 1.025641 in decimal form). Learn the step-by-step solution to add 2/6 and 9/13 using Least Common Denominator and simplification.
Exact Answer
2/6 + 9/13 = 40/39
Simplified Fraction
40/39
Mixed Number
1 1/39
Decimal Value
1.025641
Percentage
102.5641%
Step-by-Step Solution: 2/6 + 9/13
Step 1
Find the Least Common Denominator (LCD)
The denominators 6 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 6 × 13 = 78.
LCD(6, 13) = 78
Step 2
Convert to Equivalent Fractions with Common Denominator 78
Multiply the numerator and denominator of 2/6 by 13, and multiply the numerator and denominator of 9/13 by 6 so both fractions share the common base 78.
2 × 13/6 × 13 = 26/78 and 9 × 6/13 × 6 = 54/78
Step 3
Add the Numerators
Now add the numerators (26 + 54 = 80) and keep the common denominator 78 unchanged.
26 + 54/78 = 80/78
Step 4
Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 80 and 78, which is 2. Divide both the numerator and denominator by 2.
80 ÷ 2/78 ÷ 2 = 40/39
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (40) is greater than the denominator (39), divide 40 by 39: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/39.
40/39 = 11/39
Step 6
Decimal & Percentage Representation
Dividing the numerator 40 by denominator 39 produces a repeating decimal (approximately 1.025641, or 102.5641%).
40 ÷ 39 = 1.025641 (102.5641%)
Visual Representation
The diagram below illustrates 2/6 plus 9/13 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 40/39 |
| Mixed Number Form | 1 1/39 |
| Decimal Form | 1.025641 |
| Percentage | 102.5641% |
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Frequently Asked Questions
What is 2/6 plus 9/13 as a fraction?
2/6 + 9/13 in simplest fraction form is 40/39 (or 1 1/39 as a mixed number).
What is 2/6 plus 9/13 as a decimal?
2/6 + 9/13 converted to a decimal is 1.025641.
What is 2/6 plus 9/13 as a percentage?
2/6 + 9/13 expressed as a percentage is 102.5641%.
How do you write 2/6 plus 9/13 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 40/39 can be written as the mixed number 1 1/39.
Does 2/6 plus 9/13 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.025641...) because the denominator contains prime factors other than 2 and 5.