What is 2/26 plus 3/7? (Answer: 46/91)

Exact Answer

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Problem: What is 2/26 plus 3/7?
Formula / Expression: 2/26 + 3/7
Final Answer: 46/91
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 182
Multiply the numerator and denominator of 2/26 by 7, and multiply the numerator and denominator of 3/7 by 26 so both fractions share the common base 182.
Working: 2 × 7/26 × 7 = 14/182 and 3 × 26/7 × 26 = 78/182

Step 3: Add the Numerators
Now add the numerators (14 + 78 = 92) and keep the common denominator 182 unchanged.
Working: 14 + 78/182 = 92/182

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 92 and 182, which is 2. Divide both the numerator and denominator by 2.
Working: 92 ÷ 2/182 ÷ 2 = 46/91

Step 5: Decimal & Percentage Representation
Dividing the numerator 46 by denominator 91 produces a repeating decimal (approximately 0.505495, or 50.5495%).
Working: 46 ÷ 91 = 0.505495 (50.5495%)

Key Values:
- Simplified Fraction: 46/91
- Mixed Number Form: 46/91
- Decimal Value: 0.505495
- Percentage: 50.5495%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-26-plus-3-7/
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2/26 + 3/7 = 46/91

Simplified Fraction

46/91

Mixed Number

Proper (46/91)

Decimal Value

0.505495

Percentage

50.5495%

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Step-by-Step Solution: 2/26 + 3/7

Step 1

Find the Least Common Denominator (LCD)

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

LCD(26, 7) = 182

Step 2

Convert to Equivalent Fractions with Common Denominator 182

Multiply the numerator and denominator of 2/26 by 7, and multiply the numerator and denominator of 3/7 by 26 so both fractions share the common base 182.

2 × 7/26 × 7 = 14/182 and 3 × 26/7 × 26 = 78/182

Step 3

Add the Numerators

Now add the numerators (14 + 78 = 92) and keep the common denominator 182 unchanged.

14 + 78/182 = 92/182

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 92 and 182, which is 2. Divide both the numerator and denominator by 2.

92 ÷ 2/182 ÷ 2 = 46/91

Step 5

Decimal & Percentage Representation

Dividing the numerator 46 by denominator 91 produces a repeating decimal (approximately 0.505495, or 50.5495%).

46 ÷ 91 = 0.505495 (50.5495%)

Visual Representation

The diagram below illustrates 2/26 plus 3/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`46/91`
Mixed Number Form	`46/91`
Decimal Form	`0.505495`
Percentage	`50.5495%`

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Frequently Asked Questions

What is 2/26 plus 3/7 as a fraction?

2/26 + 3/7 in simplest fraction form is 46/91.

What is 2/26 plus 3/7 as a decimal?

2/26 + 3/7 converted to a decimal is 0.505495.

What is 2/26 plus 3/7 as a percentage?

2/26 + 3/7 expressed as a percentage is 50.5495%.

Does 2/26 plus 3/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.505495...) because the denominator contains prime factors other than 2 and 5.