What is 2/9 plus 7/26?
2/9 plus 7/26 equals 115/234 (or 0.491453 in decimal form). Learn the step-by-step solution to add 2/9 and 7/26 using Least Common Denominator and simplification.
Exact Answer
2/9 + 7/26 = 115/234
Simplified Fraction
115/234
Mixed Number
Proper (115/234)
Decimal Value
0.491453
Percentage
49.1453%
Step-by-Step Solution: 2/9 + 7/26
Step 1
Find the Least Common Denominator (LCD)
The denominators 9 and 26 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 26 = 234.
LCD(9, 26) = 234
Step 2
Convert to Equivalent Fractions with Common Denominator 234
Multiply the numerator and denominator of 2/9 by 26, and multiply the numerator and denominator of 7/26 by 9 so both fractions share the common base 234.
2 × 26/9 × 26 = 52/234 and 7 × 9/26 × 9 = 63/234
Step 3
Add the Numerators
Now add the numerators (52 + 63 = 115) and keep the common denominator 234 unchanged.
52 + 63/234 = 115/234
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 115 and 234 is 1, confirming that 115/234 cannot be reduced further—it is already in its simplest irreducible form.
115/234
Step 5
Decimal & Percentage Representation
Dividing the numerator 115 by denominator 234 produces a repeating decimal (approximately 0.491453, or 49.1453%).
115 ÷ 234 = 0.491453 (49.1453%)
Visual Representation
The diagram below illustrates 2/9 plus 7/26 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 115/234 |
| Mixed Number Form | 115/234 |
| Decimal Form | 0.491453 |
| Percentage | 49.1453% |
Was this solution helpful?
Help us improve our free step-by-step tools
Frequently Asked Questions
What is 2/9 plus 7/26 as a fraction?
2/9 + 7/26 in simplest fraction form is 115/234.
What is 2/9 plus 7/26 as a decimal?
2/9 + 7/26 converted to a decimal is 0.491453.
What is 2/9 plus 7/26 as a percentage?
2/9 + 7/26 expressed as a percentage is 49.1453%.
Does 2/9 plus 7/26 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 0.491453...) because the denominator contains prime factors other than 2 and 5.