What is 2/13 plus 2/8? (Answer: 21/52)

Exact Answer

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Problem: What is 2/13 plus 2/8?
Formula / Expression: 2/13 + 2/8
Final Answer: 21/52
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 13 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 8 = 104.
Working: LCD(13, 8) = 104

Step 2: Convert to Equivalent Fractions with Common Denominator 104
Multiply the numerator and denominator of 2/13 by 8, and multiply the numerator and denominator of 2/8 by 13 so both fractions share the common base 104.
Working: 2 × 8/13 × 8 = 16/104 and 2 × 13/8 × 13 = 26/104

Step 3: Add the Numerators
Now add the numerators (16 + 26 = 42) and keep the common denominator 104 unchanged.
Working: 16 + 26/104 = 42/104

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 42 and 104, which is 2. Divide both the numerator and denominator by 2.
Working: 42 ÷ 2/104 ÷ 2 = 21/52

Step 5: Decimal & Percentage Representation
Dividing the numerator 21 by denominator 52 produces a repeating decimal (approximately 0.403846, or 40.3846%).
Working: 21 ÷ 52 = 0.403846 (40.3846%)

Key Values:
- Simplified Fraction: 21/52
- Mixed Number Form: 21/52
- Decimal Value: 0.403846
- Percentage: 40.3846%

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Solved with FractionsCalc:
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2/13 + 2/8 = 21/52

Simplified Fraction

21/52

Mixed Number

Proper (21/52)

Decimal Value

0.403846

Percentage

40.3846%

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Step-by-Step Solution: 2/13 + 2/8

Step 1

Find the Least Common Denominator (LCD)

The denominators 13 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 8 = 104.

LCD(13, 8) = 104

Step 2

Convert to Equivalent Fractions with Common Denominator 104

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

2 × 8/13 × 8 = 16/104 and 2 × 13/8 × 13 = 26/104

Step 3

Add the Numerators

Now add the numerators (16 + 26 = 42) and keep the common denominator 104 unchanged.

16 + 26/104 = 42/104

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 42 and 104, which is 2. Divide both the numerator and denominator by 2.

42 ÷ 2/104 ÷ 2 = 21/52

Step 5

Decimal & Percentage Representation

Dividing the numerator 21 by denominator 52 produces a repeating decimal (approximately 0.403846, or 40.3846%).

21 ÷ 52 = 0.403846 (40.3846%)

Visual Representation

The diagram below illustrates 2/13 plus 2/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`21/52`
Mixed Number Form	`21/52`
Decimal Form	`0.403846`
Percentage	`40.3846%`

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Frequently Asked Questions

What is 2/13 plus 2/8 as a fraction?

2/13 + 2/8 in simplest fraction form is 21/52.

What is 2/13 plus 2/8 as a decimal?

2/13 + 2/8 converted to a decimal is 0.403846.

What is 2/13 plus 2/8 as a percentage?

2/13 + 2/8 expressed as a percentage is 40.3846%.

Does 2/13 plus 2/8 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.403846...) because the denominator contains prime factors other than 2 and 5.