What is 3/26 plus 4/9? (Answer: 131/234)

Exact Answer

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Problem: What is 3/26 plus 4/9?
Formula / Expression: 3/26 + 4/9
Final Answer: 131/234
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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 3/26 by 9, and multiply the numerator and denominator of 4/9 by 26 so both fractions share the common base 234.
Working: 3 × 9/26 × 9 = 27/234 and 4 × 26/9 × 26 = 104/234

Step 3: Add the Numerators
Now add the numerators (27 + 104 = 131) and keep the common denominator 234 unchanged.
Working: 27 + 104/234 = 131/234

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 131 and 234 is 1, confirming that 131/234 cannot be reduced further—it is already in its simplest irreducible form.
Working: 131/234

Step 5: Decimal & Percentage Representation
Dividing the numerator 131 by denominator 234 produces a repeating decimal (approximately 0.559829, or 55.9829%).
Working: 131 ÷ 234 = 0.559829 (55.9829%)

Key Values:
- Simplified Fraction: 131/234
- Mixed Number Form: 131/234
- Decimal Value: 0.559829
- Percentage: 55.9829%

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Solved with FractionsCalc:
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3/26 + 4/9 = 131/234

Simplified Fraction

131/234

Mixed Number

Proper (131/234)

Decimal Value

0.559829

Percentage

55.9829%

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Step-by-Step Solution: 3/26 + 4/9

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 3/26 by 9, and multiply the numerator and denominator of 4/9 by 26 so both fractions share the common base 234.

3 × 9/26 × 9 = 27/234 and 4 × 26/9 × 26 = 104/234

Step 3

Add the Numerators

Now add the numerators (27 + 104 = 131) and keep the common denominator 234 unchanged.

27 + 104/234 = 131/234

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 131 and 234 is 1, confirming that 131/234 cannot be reduced further—it is already in its simplest irreducible form.

131/234

Step 5

Decimal & Percentage Representation

Dividing the numerator 131 by denominator 234 produces a repeating decimal (approximately 0.559829, or 55.9829%).

131 ÷ 234 = 0.559829 (55.9829%)

Visual Representation

The diagram below illustrates 3/26 plus 4/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`131/234`
Mixed Number Form	`131/234`
Decimal Form	`0.559829`
Percentage	`55.9829%`

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Frequently Asked Questions

What is 3/26 plus 4/9 as a fraction?

3/26 + 4/9 in simplest fraction form is 131/234.

What is 3/26 plus 4/9 as a decimal?

3/26 + 4/9 converted to a decimal is 0.559829.

What is 3/26 plus 4/9 as a percentage?

3/26 + 4/9 expressed as a percentage is 55.9829%.

Does 3/26 plus 4/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.559829...) because the denominator contains prime factors other than 2 and 5.