What is 2/26 plus 2/9? (Answer: 35/117)

Exact Answer

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Problem: What is 2/26 plus 2/9?
Formula / Expression: 2/26 + 2/9
Final Answer: 35/117
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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 2/9 by 26 so both fractions share the common base 234.
Working: 2 × 9/26 × 9 = 18/234 and 2 × 26/9 × 26 = 52/234

Step 3: Add the Numerators
Now add the numerators (18 + 52 = 70) and keep the common denominator 234 unchanged.
Working: 18 + 52/234 = 70/234

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 70 and 234, which is 2. Divide both the numerator and denominator by 2.
Working: 70 ÷ 2/234 ÷ 2 = 35/117

Step 5: Decimal & Percentage Representation
Dividing the numerator 35 by denominator 117 produces a repeating decimal (approximately 0.299145, or 29.9145%).
Working: 35 ÷ 117 = 0.299145 (29.9145%)

Key Values:
- Simplified Fraction: 35/117
- Mixed Number Form: 35/117
- Decimal Value: 0.299145
- Percentage: 29.9145%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-26-plus-2-9/
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2/26 + 2/9 = 35/117

Simplified Fraction

35/117

Mixed Number

Proper (35/117)

Decimal Value

0.299145

Percentage

29.9145%

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Step-by-Step Solution: 2/26 + 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 2/26 by 9, and multiply the numerator and denominator of 2/9 by 26 so both fractions share the common base 234.

2 × 9/26 × 9 = 18/234 and 2 × 26/9 × 26 = 52/234

Step 3

Add the Numerators

Now add the numerators (18 + 52 = 70) and keep the common denominator 234 unchanged.

18 + 52/234 = 70/234

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 70 and 234, which is 2. Divide both the numerator and denominator by 2.

70 ÷ 2/234 ÷ 2 = 35/117

Step 5

Decimal & Percentage Representation

Dividing the numerator 35 by denominator 117 produces a repeating decimal (approximately 0.299145, or 29.9145%).

35 ÷ 117 = 0.299145 (29.9145%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`35/117`
Mixed Number Form	`35/117`
Decimal Form	`0.299145`
Percentage	`29.9145%`

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Frequently Asked Questions

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

2/26 + 2/9 in simplest fraction form is 35/117.

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

2/26 + 2/9 converted to a decimal is 0.299145.

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

2/26 + 2/9 expressed as a percentage is 29.9145%.

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

It results in a repeating decimal (approximately 0.299145...) because the denominator contains prime factors other than 2 and 5.