What is 2/9 plus 10/26? (Answer: 71/117)

Exact Answer

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Problem: What is 2/9 plus 10/26?
Formula / Expression: 2/9 + 10/26
Final Answer: 71/117
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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 10/26 by 9 so both fractions share the common base 234.
Working: 2 × 26/9 × 26 = 52/234 and 10 × 9/26 × 9 = 90/234

Step 3: Add the Numerators
Now add the numerators (52 + 90 = 142) and keep the common denominator 234 unchanged.
Working: 52 + 90/234 = 142/234

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 142 and 234, which is 2. Divide both the numerator and denominator by 2.
Working: 142 ÷ 2/234 ÷ 2 = 71/117

Step 5: Decimal & Percentage Representation
Dividing the numerator 71 by denominator 117 produces a repeating decimal (approximately 0.606838, or 60.6838%).
Working: 71 ÷ 117 = 0.606838 (60.6838%)

Key Values:
- Simplified Fraction: 71/117
- Mixed Number Form: 71/117
- Decimal Value: 0.606838
- Percentage: 60.6838%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-9-plus-10-26/
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2/9 + 10/26 = 71/117

Simplified Fraction

71/117

Mixed Number

Proper (71/117)

Decimal Value

0.606838

Percentage

60.6838%

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Step-by-Step Solution: 2/9 + 10/26

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 10/26 by 9 so both fractions share the common base 234.

2 × 26/9 × 26 = 52/234 and 10 × 9/26 × 9 = 90/234

Step 3

Add the Numerators

Now add the numerators (52 + 90 = 142) and keep the common denominator 234 unchanged.

52 + 90/234 = 142/234

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 142 and 234, which is 2. Divide both the numerator and denominator by 2.

142 ÷ 2/234 ÷ 2 = 71/117

Step 5

Decimal & Percentage Representation

Dividing the numerator 71 by denominator 117 produces a repeating decimal (approximately 0.606838, or 60.6838%).

71 ÷ 117 = 0.606838 (60.6838%)

Visual Representation

The diagram below illustrates 2/9 plus 10/26 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`71/117`
Mixed Number Form	`71/117`
Decimal Form	`0.606838`
Percentage	`60.6838%`

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Frequently Asked Questions

What is 2/9 plus 10/26 as a fraction?

2/9 + 10/26 in simplest fraction form is 71/117.

What is 2/9 plus 10/26 as a decimal?

2/9 + 10/26 converted to a decimal is 0.606838.

What is 2/9 plus 10/26 as a percentage?

2/9 + 10/26 expressed as a percentage is 60.6838%.

Does 2/9 plus 10/26 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.606838...) because the denominator contains prime factors other than 2 and 5.