What is 2/8 plus 4/13? (Answer: 29/52)

Exact Answer

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Problem: What is 2/8 plus 4/13?
Formula / Expression: 2/8 + 4/13
Final Answer: 29/52
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 104
Multiply the numerator and denominator of 2/8 by 13, and multiply the numerator and denominator of 4/13 by 8 so both fractions share the common base 104.
Working: 2 × 13/8 × 13 = 26/104 and 4 × 8/13 × 8 = 32/104

Step 3: Add the Numerators
Now add the numerators (26 + 32 = 58) and keep the common denominator 104 unchanged.
Working: 26 + 32/104 = 58/104

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 58 and 104, which is 2. Divide both the numerator and denominator by 2.
Working: 58 ÷ 2/104 ÷ 2 = 29/52

Step 5: Decimal & Percentage Representation
Dividing the numerator 29 by denominator 52 produces a repeating decimal (approximately 0.557692, or 55.7692%).
Working: 29 ÷ 52 = 0.557692 (55.7692%)

Key Values:
- Simplified Fraction: 29/52
- Mixed Number Form: 29/52
- Decimal Value: 0.557692
- Percentage: 55.7692%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-8-plus-4-13/
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2/8 + 4/13 = 29/52

Simplified Fraction

29/52

Mixed Number

Proper (29/52)

Decimal Value

0.557692

Percentage

55.7692%

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Step-by-Step Solution: 2/8 + 4/13

Step 1

Find the Least Common Denominator (LCD)

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

LCD(8, 13) = 104

Step 2

Convert to Equivalent Fractions with Common Denominator 104

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

2 × 13/8 × 13 = 26/104 and 4 × 8/13 × 8 = 32/104

Step 3

Add the Numerators

Now add the numerators (26 + 32 = 58) and keep the common denominator 104 unchanged.

26 + 32/104 = 58/104

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 58 and 104, which is 2. Divide both the numerator and denominator by 2.

58 ÷ 2/104 ÷ 2 = 29/52

Step 5

Decimal & Percentage Representation

Dividing the numerator 29 by denominator 52 produces a repeating decimal (approximately 0.557692, or 55.7692%).

29 ÷ 52 = 0.557692 (55.7692%)

Visual Representation

The diagram below illustrates 2/8 plus 4/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`29/52`
Mixed Number Form	`29/52`
Decimal Form	`0.557692`
Percentage	`55.7692%`

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Frequently Asked Questions

What is 2/8 plus 4/13 as a fraction?

2/8 + 4/13 in simplest fraction form is 29/52.

What is 2/8 plus 4/13 as a decimal?

2/8 + 4/13 converted to a decimal is 0.557692.

What is 2/8 plus 4/13 as a percentage?

2/8 + 4/13 expressed as a percentage is 55.7692%.

Does 2/8 plus 4/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.557692...) because the denominator contains prime factors other than 2 and 5.