What is 2/8 plus 5/13? (Answer: 33/52)

Exact Answer

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Problem: What is 2/8 plus 5/13?
Formula / Expression: 2/8 + 5/13
Final Answer: 33/52
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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 5/13 by 8 so both fractions share the common base 104.
Working: 2 × 13/8 × 13 = 26/104 and 5 × 8/13 × 8 = 40/104

Step 3: Add the Numerators
Now add the numerators (26 + 40 = 66) and keep the common denominator 104 unchanged.
Working: 26 + 40/104 = 66/104

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 66 and 104, which is 2. Divide both the numerator and denominator by 2.
Working: 66 ÷ 2/104 ÷ 2 = 33/52

Step 5: Decimal & Percentage Representation
Dividing the numerator 33 by denominator 52 produces a repeating decimal (approximately 0.634615, or 63.4615%).
Working: 33 ÷ 52 = 0.634615 (63.4615%)

Key Values:
- Simplified Fraction: 33/52
- Mixed Number Form: 33/52
- Decimal Value: 0.634615
- Percentage: 63.4615%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-8-plus-5-13/
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2/8 + 5/13 = 33/52

Simplified Fraction

33/52

Mixed Number

Proper (33/52)

Decimal Value

0.634615

Percentage

63.4615%

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Step-by-Step Solution: 2/8 + 5/13

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 5/13 by 8 so both fractions share the common base 104.

2 × 13/8 × 13 = 26/104 and 5 × 8/13 × 8 = 40/104

Step 3

Add the Numerators

Now add the numerators (26 + 40 = 66) and keep the common denominator 104 unchanged.

26 + 40/104 = 66/104

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 66 and 104, which is 2. Divide both the numerator and denominator by 2.

66 ÷ 2/104 ÷ 2 = 33/52

Step 5

Decimal & Percentage Representation

Dividing the numerator 33 by denominator 52 produces a repeating decimal (approximately 0.634615, or 63.4615%).

33 ÷ 52 = 0.634615 (63.4615%)

Visual Representation

The diagram below illustrates 2/8 plus 5/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`33/52`
Mixed Number Form	`33/52`
Decimal Form	`0.634615`
Percentage	`63.4615%`

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Frequently Asked Questions

What is 2/8 plus 5/13 as a fraction?

2/8 + 5/13 in simplest fraction form is 33/52.

What is 2/8 plus 5/13 as a decimal?

2/8 + 5/13 converted to a decimal is 0.634615.

What is 2/8 plus 5/13 as a percentage?

2/8 + 5/13 expressed as a percentage is 63.4615%.

Does 2/8 plus 5/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.634615...) because the denominator contains prime factors other than 2 and 5.