What is 2/26 plus 3/9? (Answer: 16/39)

Exact Answer

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Problem: What is 2/26 plus 3/9?
Formula / Expression: 2/26 + 3/9
Final Answer: 16/39
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 26 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 26 × 9 = 234.
Working: LCD(26, 9) = 234

Step 2: Convert to Equivalent Fractions with Common Denominator 234
Multiply the numerator and denominator of 2/26 by 9, and multiply the numerator and denominator of 3/9 by 26 so both fractions share the common base 234.
Working: 2 × 9/26 × 9 = 18/234 and 3 × 26/9 × 26 = 78/234

Step 3: Add the Numerators
Now add the numerators (18 + 78 = 96) and keep the common denominator 234 unchanged.
Working: 18 + 78/234 = 96/234

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 96 and 234, which is 6. Divide both the numerator and denominator by 6.
Working: 96 ÷ 6/234 ÷ 6 = 16/39

Step 5: Decimal & Percentage Representation
Dividing the numerator 16 by denominator 39 produces a repeating decimal (approximately 0.410256, or 41.0256%).
Working: 16 ÷ 39 = 0.410256 (41.0256%)

Key Values:
- Simplified Fraction: 16/39
- Mixed Number Form: 16/39
- Decimal Value: 0.410256
- Percentage: 41.0256%

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Solved with FractionsCalc:
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2/26 + 3/9 = 16/39

Simplified Fraction

16/39

Mixed Number

Proper (16/39)

Decimal Value

0.410256

Percentage

41.0256%

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Step-by-Step Solution: 2/26 + 3/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 26 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 26 × 9 = 234.

LCD(26, 9) = 234

Step 2

Convert to Equivalent Fractions with Common Denominator 234

Multiply the numerator and denominator of 2/26 by 9, and multiply the numerator and denominator of 3/9 by 26 so both fractions share the common base 234.

2 × 9/26 × 9 = 18/234 and 3 × 26/9 × 26 = 78/234

Step 3

Add the Numerators

Now add the numerators (18 + 78 = 96) and keep the common denominator 234 unchanged.

18 + 78/234 = 96/234

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 96 and 234, which is 6. Divide both the numerator and denominator by 6.

96 ÷ 6/234 ÷ 6 = 16/39

Step 5

Decimal & Percentage Representation

Dividing the numerator 16 by denominator 39 produces a repeating decimal (approximately 0.410256, or 41.0256%).

16 ÷ 39 = 0.410256 (41.0256%)

Visual Representation

The diagram below illustrates 2/26 plus 3/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`16/39`
Mixed Number Form	`16/39`
Decimal Form	`0.410256`
Percentage	`41.0256%`

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Frequently Asked Questions

What is 2/26 plus 3/9 as a fraction?

2/26 + 3/9 in simplest fraction form is 16/39.

What is 2/26 plus 3/9 as a decimal?

2/26 + 3/9 converted to a decimal is 0.410256.

What is 2/26 plus 3/9 as a percentage?

2/26 + 3/9 expressed as a percentage is 41.0256%.

Does 2/26 plus 3/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.410256...) because the denominator contains prime factors other than 2 and 5.