What is 5/26 plus 2/9? (Answer: 97/234)

Exact Answer

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Problem: What is 5/26 plus 2/9?
Formula / Expression: 5/26 + 2/9
Final Answer: 97/234
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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 5/26 by 9, and multiply the numerator and denominator of 2/9 by 26 so both fractions share the common base 234.
Working: 5 × 9/26 × 9 = 45/234 and 2 × 26/9 × 26 = 52/234

Step 3: Add the Numerators
Now add the numerators (45 + 52 = 97) and keep the common denominator 234 unchanged.
Working: 45 + 52/234 = 97/234

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 97 and 234 is 1, confirming that 97/234 cannot be reduced further—it is already in its simplest irreducible form.
Working: 97/234

Step 5: Decimal & Percentage Representation
Dividing the numerator 97 by denominator 234 produces a repeating decimal (approximately 0.41453, or 41.453%).
Working: 97 ÷ 234 = 0.41453 (41.453%)

Key Values:
- Simplified Fraction: 97/234
- Mixed Number Form: 97/234
- Decimal Value: 0.41453
- Percentage: 41.453%

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Solved with FractionsCalc:
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5/26 + 2/9 = 97/234

Simplified Fraction

97/234

Mixed Number

Proper (97/234)

Decimal Value

0.41453

Percentage

41.453%

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Step-by-Step Solution: 5/26 + 2/9

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 5/26 by 9, and multiply the numerator and denominator of 2/9 by 26 so both fractions share the common base 234.

5 × 9/26 × 9 = 45/234 and 2 × 26/9 × 26 = 52/234

Step 3

Add the Numerators

Now add the numerators (45 + 52 = 97) and keep the common denominator 234 unchanged.

45 + 52/234 = 97/234

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 97 and 234 is 1, confirming that 97/234 cannot be reduced further—it is already in its simplest irreducible form.

97/234

Step 5

Decimal & Percentage Representation

Dividing the numerator 97 by denominator 234 produces a repeating decimal (approximately 0.41453, or 41.453%).

97 ÷ 234 = 0.41453 (41.453%)

Visual Representation

The diagram below illustrates 5/26 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`97/234`
Mixed Number Form	`97/234`
Decimal Form	`0.41453`
Percentage	`41.453%`

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Frequently Asked Questions

What is 5/26 plus 2/9 as a fraction?

5/26 + 2/9 in simplest fraction form is 97/234.

What is 5/26 plus 2/9 as a decimal?

5/26 + 2/9 converted to a decimal is 0.41453.

What is 5/26 plus 2/9 as a percentage?

5/26 + 2/9 expressed as a percentage is 41.453%.

Does 5/26 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.41453...) because the denominator contains prime factors other than 2 and 5.