What is 2/9 plus 9/26? (Answer: 133/234)

Exact Answer

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Problem: What is 2/9 plus 9/26?
Formula / Expression: 2/9 + 9/26
Final Answer: 133/234
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Step-by-Step Solution:

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.
Working: 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 9/26 by 9 so both fractions share the common base 234.
Working: 2 × 26/9 × 26 = 52/234 and 9 × 9/26 × 9 = 81/234

Step 3: Add the Numerators
Now add the numerators (52 + 81 = 133) and keep the common denominator 234 unchanged.
Working: 52 + 81/234 = 133/234

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 133 and 234 is 1, confirming that 133/234 cannot be reduced further—it is already in its simplest irreducible form.
Working: 133/234

Step 5: Decimal & Percentage Representation
Dividing the numerator 133 by denominator 234 produces a repeating decimal (approximately 0.568376, or 56.8376%).
Working: 133 ÷ 234 = 0.568376 (56.8376%)

Key Values:
- Simplified Fraction: 133/234
- Mixed Number Form: 133/234
- Decimal Value: 0.568376
- Percentage: 56.8376%

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Solved with FractionsCalc:
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2/9 + 9/26 = 133/234

Simplified Fraction

133/234

Mixed Number

Proper (133/234)

Decimal Value

0.568376

Percentage

56.8376%

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

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 9/26 by 9 so both fractions share the common base 234.

2 × 26/9 × 26 = 52/234 and 9 × 9/26 × 9 = 81/234

Step 3

Add the Numerators

Now add the numerators (52 + 81 = 133) and keep the common denominator 234 unchanged.

52 + 81/234 = 133/234

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 133 and 234 is 1, confirming that 133/234 cannot be reduced further—it is already in its simplest irreducible form.

133/234

Step 5

Decimal & Percentage Representation

Dividing the numerator 133 by denominator 234 produces a repeating decimal (approximately 0.568376, or 56.8376%).

133 ÷ 234 = 0.568376 (56.8376%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`133/234`
Mixed Number Form	`133/234`
Decimal Form	`0.568376`
Percentage	`56.8376%`

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Frequently Asked Questions

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

2/9 + 9/26 in simplest fraction form is 133/234.

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

2/9 + 9/26 converted to a decimal is 0.568376.

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

2/9 + 9/26 expressed as a percentage is 56.8376%.

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

It results in a repeating decimal (approximately 0.568376...) because the denominator contains prime factors other than 2 and 5.