What is 2/26 plus 3/8? (Answer: 47/104)

Exact Answer

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Problem: What is 2/26 plus 3/8?
Formula / Expression: 2/26 + 3/8
Final Answer: 47/104
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 26 and 8 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 104 (which is smaller than their product 26 × 8 = 208, keeping the calculation simpler).
Working: LCD(26, 8) = 104

Step 2: Convert to Equivalent Fractions with Common Denominator 104
Multiply the numerator and denominator of 2/26 by 4, and multiply the numerator and denominator of 3/8 by 13 so both fractions share the common base 104.
Working: 2 × 4/26 × 4 = 8/104 and 3 × 13/8 × 13 = 39/104

Step 3: Add the Numerators
Now add the numerators (8 + 39 = 47) and keep the common denominator 104 unchanged.
Working: 8 + 39/104 = 47/104

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 47 and 104 is 1, confirming that 47/104 cannot be reduced further—it is already in its simplest irreducible form.
Working: 47/104

Step 5: Decimal & Percentage Representation
Dividing the numerator 47 by denominator 104 produces a repeating decimal (approximately 0.451923, or 45.1923%).
Working: 47 ÷ 104 = 0.451923 (45.1923%)

Key Values:
- Simplified Fraction: 47/104
- Mixed Number Form: 47/104
- Decimal Value: 0.451923
- Percentage: 45.1923%

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Solved with FractionsCalc:
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2/26 + 3/8 = 47/104

Simplified Fraction

47/104

Mixed Number

Proper (47/104)

Decimal Value

0.451923

Percentage

45.1923%

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Step-by-Step Solution: 2/26 + 3/8

Step 1

Find the Least Common Denominator (LCD)

The denominators 26 and 8 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 104 (which is smaller than their product 26 × 8 = 208, keeping the calculation simpler).

LCD(26, 8) = 104

Step 2

Convert to Equivalent Fractions with Common Denominator 104

Multiply the numerator and denominator of 2/26 by 4, and multiply the numerator and denominator of 3/8 by 13 so both fractions share the common base 104.

2 × 4/26 × 4 = 8/104 and 3 × 13/8 × 13 = 39/104

Step 3

Add the Numerators

Now add the numerators (8 + 39 = 47) and keep the common denominator 104 unchanged.

8 + 39/104 = 47/104

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 47 and 104 is 1, confirming that 47/104 cannot be reduced further—it is already in its simplest irreducible form.

47/104

Step 5

Decimal & Percentage Representation

Dividing the numerator 47 by denominator 104 produces a repeating decimal (approximately 0.451923, or 45.1923%).

47 ÷ 104 = 0.451923 (45.1923%)

Visual Representation

The diagram below illustrates 2/26 plus 3/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`47/104`
Mixed Number Form	`47/104`
Decimal Form	`0.451923`
Percentage	`45.1923%`

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Frequently Asked Questions

What is 2/26 plus 3/8 as a fraction?

2/26 + 3/8 in simplest fraction form is 47/104.

What is 2/26 plus 3/8 as a decimal?

2/26 + 3/8 converted to a decimal is 0.451923.

What is 2/26 plus 3/8 as a percentage?

2/26 + 3/8 expressed as a percentage is 45.1923%.

Does 2/26 plus 3/8 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.451923...) because the denominator contains prime factors other than 2 and 5.