What is 3/26 plus 2/8? (Answer: 19/52)

Exact Answer

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Problem: What is 3/26 plus 2/8?
Formula / Expression: 3/26 + 2/8
Final Answer: 19/52
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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 3/26 by 4, and multiply the numerator and denominator of 2/8 by 13 so both fractions share the common base 104.
Working: 3 × 4/26 × 4 = 12/104 and 2 × 13/8 × 13 = 26/104

Step 3: Add the Numerators
Now add the numerators (12 + 26 = 38) and keep the common denominator 104 unchanged.
Working: 12 + 26/104 = 38/104

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 38 and 104, which is 2. Divide both the numerator and denominator by 2.
Working: 38 ÷ 2/104 ÷ 2 = 19/52

Step 5: Decimal & Percentage Representation
Dividing the numerator 19 by denominator 52 produces a repeating decimal (approximately 0.365385, or 36.5385%).
Working: 19 ÷ 52 = 0.365385 (36.5385%)

Key Values:
- Simplified Fraction: 19/52
- Mixed Number Form: 19/52
- Decimal Value: 0.365385
- Percentage: 36.5385%

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Solved with FractionsCalc:
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3/26 + 2/8 = 19/52

Simplified Fraction

19/52

Mixed Number

Proper (19/52)

Decimal Value

0.365385

Percentage

36.5385%

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

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

3 × 4/26 × 4 = 12/104 and 2 × 13/8 × 13 = 26/104

Step 3

Add the Numerators

Now add the numerators (12 + 26 = 38) and keep the common denominator 104 unchanged.

12 + 26/104 = 38/104

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 38 and 104, which is 2. Divide both the numerator and denominator by 2.

38 ÷ 2/104 ÷ 2 = 19/52

Step 5

Decimal & Percentage Representation

Dividing the numerator 19 by denominator 52 produces a repeating decimal (approximately 0.365385, or 36.5385%).

19 ÷ 52 = 0.365385 (36.5385%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`19/52`
Mixed Number Form	`19/52`
Decimal Form	`0.365385`
Percentage	`36.5385%`

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Frequently Asked Questions

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

3/26 + 2/8 in simplest fraction form is 19/52.

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

3/26 + 2/8 converted to a decimal is 0.365385.

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

3/26 + 2/8 expressed as a percentage is 36.5385%.

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

It results in a repeating decimal (approximately 0.365385...) because the denominator contains prime factors other than 2 and 5.