What is 2/39 plus 2/8? (Answer: 47/156)

Exact Answer

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Problem: What is 2/39 plus 2/8?
Formula / Expression: 2/39 + 2/8
Final Answer: 47/156
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 39 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 39 × 8 = 312.
Working: LCD(39, 8) = 312

Step 2: Convert to Equivalent Fractions with Common Denominator 312
Multiply the numerator and denominator of 2/39 by 8, and multiply the numerator and denominator of 2/8 by 39 so both fractions share the common base 312.
Working: 2 × 8/39 × 8 = 16/312 and 2 × 39/8 × 39 = 78/312

Step 3: Add the Numerators
Now add the numerators (16 + 78 = 94) and keep the common denominator 312 unchanged.
Working: 16 + 78/312 = 94/312

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 94 and 312, which is 2. Divide both the numerator and denominator by 2.
Working: 94 ÷ 2/312 ÷ 2 = 47/156

Step 5: Decimal & Percentage Representation
Dividing the numerator 47 by denominator 156 produces a repeating decimal (approximately 0.301282, or 30.1282%).
Working: 47 ÷ 156 = 0.301282 (30.1282%)

Key Values:
- Simplified Fraction: 47/156
- Mixed Number Form: 47/156
- Decimal Value: 0.301282
- Percentage: 30.1282%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-39-plus-2-8/
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2/39 + 2/8 = 47/156

Simplified Fraction

47/156

Mixed Number

Proper (47/156)

Decimal Value

0.301282

Percentage

30.1282%

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Step-by-Step Solution: 2/39 + 2/8

Step 1

Find the Least Common Denominator (LCD)

The denominators 39 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 39 × 8 = 312.

LCD(39, 8) = 312

Step 2

Convert to Equivalent Fractions with Common Denominator 312

Multiply the numerator and denominator of 2/39 by 8, and multiply the numerator and denominator of 2/8 by 39 so both fractions share the common base 312.

2 × 8/39 × 8 = 16/312 and 2 × 39/8 × 39 = 78/312

Step 3

Add the Numerators

Now add the numerators (16 + 78 = 94) and keep the common denominator 312 unchanged.

16 + 78/312 = 94/312

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 94 and 312, which is 2. Divide both the numerator and denominator by 2.

94 ÷ 2/312 ÷ 2 = 47/156

Step 5

Decimal & Percentage Representation

Dividing the numerator 47 by denominator 156 produces a repeating decimal (approximately 0.301282, or 30.1282%).

47 ÷ 156 = 0.301282 (30.1282%)

Visual Representation

The diagram below illustrates 2/39 plus 2/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`47/156`
Mixed Number Form	`47/156`
Decimal Form	`0.301282`
Percentage	`30.1282%`

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Frequently Asked Questions

What is 2/39 plus 2/8 as a fraction?

2/39 + 2/8 in simplest fraction form is 47/156.

What is 2/39 plus 2/8 as a decimal?

2/39 + 2/8 converted to a decimal is 0.301282.

What is 2/39 plus 2/8 as a percentage?

2/39 + 2/8 expressed as a percentage is 30.1282%.

Does 2/39 plus 2/8 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.301282...) because the denominator contains prime factors other than 2 and 5.