What is 2/13 plus 8/50? (Answer: 102/325)

Exact Answer

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Problem: What is 2/13 plus 8/50?
Formula / Expression: 2/13 + 8/50
Final Answer: 102/325
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 13 and 50 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 50 = 650.
Working: LCD(13, 50) = 650

Step 2: Convert to Equivalent Fractions with Common Denominator 650
Multiply the numerator and denominator of 2/13 by 50, and multiply the numerator and denominator of 8/50 by 13 so both fractions share the common base 650.
Working: 2 × 50/13 × 50 = 100/650 and 8 × 13/50 × 13 = 104/650

Step 3: Add the Numerators
Now add the numerators (100 + 104 = 204) and keep the common denominator 650 unchanged.
Working: 100 + 104/650 = 204/650

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 204 and 650, which is 2. Divide both the numerator and denominator by 2.
Working: 204 ÷ 2/650 ÷ 2 = 102/325

Step 5: Decimal & Percentage Representation
Dividing the numerator 102 by denominator 325 produces a repeating decimal (approximately 0.313846, or 31.3846%).
Working: 102 ÷ 325 = 0.313846 (31.3846%)

Key Values:
- Simplified Fraction: 102/325
- Mixed Number Form: 102/325
- Decimal Value: 0.313846
- Percentage: 31.3846%

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Solved with FractionsCalc:
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2/13 + 8/50 = 102/325

Simplified Fraction

102/325

Mixed Number

Proper (102/325)

Decimal Value

0.313846

Percentage

31.3846%

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Step-by-Step Solution: 2/13 + 8/50

Step 1

Find the Least Common Denominator (LCD)

The denominators 13 and 50 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 50 = 650.

LCD(13, 50) = 650

Step 2

Convert to Equivalent Fractions with Common Denominator 650

Multiply the numerator and denominator of 2/13 by 50, and multiply the numerator and denominator of 8/50 by 13 so both fractions share the common base 650.

2 × 50/13 × 50 = 100/650 and 8 × 13/50 × 13 = 104/650

Step 3

Add the Numerators

Now add the numerators (100 + 104 = 204) and keep the common denominator 650 unchanged.

100 + 104/650 = 204/650

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 204 and 650, which is 2. Divide both the numerator and denominator by 2.

204 ÷ 2/650 ÷ 2 = 102/325

Step 5

Decimal & Percentage Representation

Dividing the numerator 102 by denominator 325 produces a repeating decimal (approximately 0.313846, or 31.3846%).

102 ÷ 325 = 0.313846 (31.3846%)

Visual Representation

The diagram below illustrates 2/13 plus 8/50 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`102/325`
Mixed Number Form	`102/325`
Decimal Form	`0.313846`
Percentage	`31.3846%`

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Frequently Asked Questions

What is 2/13 plus 8/50 as a fraction?

2/13 + 8/50 in simplest fraction form is 102/325.

What is 2/13 plus 8/50 as a decimal?

2/13 + 8/50 converted to a decimal is 0.313846.

What is 2/13 plus 8/50 as a percentage?

2/13 + 8/50 expressed as a percentage is 31.3846%.

Does 2/13 plus 8/50 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.313846...) because the denominator contains prime factors other than 2 and 5.