What is 2/7 plus 9/26? (Answer: 115/182)

Exact Answer

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Problem: What is 2/7 plus 9/26?
Formula / Expression: 2/7 + 9/26
Final Answer: 115/182
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 7 and 26 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 26 = 182.
Working: LCD(7, 26) = 182

Step 2: Convert to Equivalent Fractions with Common Denominator 182
Multiply the numerator and denominator of 2/7 by 26, and multiply the numerator and denominator of 9/26 by 7 so both fractions share the common base 182.
Working: 2 × 26/7 × 26 = 52/182 and 9 × 7/26 × 7 = 63/182

Step 3: Add the Numerators
Now add the numerators (52 + 63 = 115) and keep the common denominator 182 unchanged.
Working: 52 + 63/182 = 115/182

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 115 and 182 is 1, confirming that 115/182 cannot be reduced further—it is already in its simplest irreducible form.
Working: 115/182

Step 5: Decimal & Percentage Representation
Dividing the numerator 115 by denominator 182 produces a repeating decimal (approximately 0.631868, or 63.1868%).
Working: 115 ÷ 182 = 0.631868 (63.1868%)

Key Values:
- Simplified Fraction: 115/182
- Mixed Number Form: 115/182
- Decimal Value: 0.631868
- Percentage: 63.1868%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-7-plus-9-26/
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2/7 + 9/26 = 115/182

Simplified Fraction

115/182

Mixed Number

Proper (115/182)

Decimal Value

0.631868

Percentage

63.1868%

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Step-by-Step Solution: 2/7 + 9/26

Step 1

Find the Least Common Denominator (LCD)

The denominators 7 and 26 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 26 = 182.

LCD(7, 26) = 182

Step 2

Convert to Equivalent Fractions with Common Denominator 182

Multiply the numerator and denominator of 2/7 by 26, and multiply the numerator and denominator of 9/26 by 7 so both fractions share the common base 182.

2 × 26/7 × 26 = 52/182 and 9 × 7/26 × 7 = 63/182

Step 3

Add the Numerators

Now add the numerators (52 + 63 = 115) and keep the common denominator 182 unchanged.

52 + 63/182 = 115/182

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 115 and 182 is 1, confirming that 115/182 cannot be reduced further—it is already in its simplest irreducible form.

115/182

Step 5

Decimal & Percentage Representation

Dividing the numerator 115 by denominator 182 produces a repeating decimal (approximately 0.631868, or 63.1868%).

115 ÷ 182 = 0.631868 (63.1868%)

Visual Representation

The diagram below illustrates 2/7 plus 9/26 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`115/182`
Mixed Number Form	`115/182`
Decimal Form	`0.631868`
Percentage	`63.1868%`

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Frequently Asked Questions

What is 2/7 plus 9/26 as a fraction?

2/7 + 9/26 in simplest fraction form is 115/182.

What is 2/7 plus 9/26 as a decimal?

2/7 + 9/26 converted to a decimal is 0.631868.

What is 2/7 plus 9/26 as a percentage?

2/7 + 9/26 expressed as a percentage is 63.1868%.

Does 2/7 plus 9/26 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.631868...) because the denominator contains prime factors other than 2 and 5.