What is 2/8 plus 5/19? (Answer: 39/76)

Exact Answer

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Problem: What is 2/8 plus 5/19?
Formula / Expression: 2/8 + 5/19
Final Answer: 39/76
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 8 and 19 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 8 × 19 = 152.
Working: LCD(8, 19) = 152

Step 2: Convert to Equivalent Fractions with Common Denominator 152
Multiply the numerator and denominator of 2/8 by 19, and multiply the numerator and denominator of 5/19 by 8 so both fractions share the common base 152.
Working: 2 × 19/8 × 19 = 38/152 and 5 × 8/19 × 8 = 40/152

Step 3: Add the Numerators
Now add the numerators (38 + 40 = 78) and keep the common denominator 152 unchanged.
Working: 38 + 40/152 = 78/152

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 78 and 152, which is 2. Divide both the numerator and denominator by 2.
Working: 78 ÷ 2/152 ÷ 2 = 39/76

Step 5: Decimal & Percentage Representation
Dividing the numerator 39 by denominator 76 produces a repeating decimal (approximately 0.513158, or 51.3158%).
Working: 39 ÷ 76 = 0.513158 (51.3158%)

Key Values:
- Simplified Fraction: 39/76
- Mixed Number Form: 39/76
- Decimal Value: 0.513158
- Percentage: 51.3158%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-8-plus-5-19/
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2/8 + 5/19 = 39/76

Simplified Fraction

39/76

Mixed Number

Proper (39/76)

Decimal Value

0.513158

Percentage

51.3158%

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Step-by-Step Solution: 2/8 + 5/19

Step 1

Find the Least Common Denominator (LCD)

The denominators 8 and 19 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 8 × 19 = 152.

LCD(8, 19) = 152

Step 2

Convert to Equivalent Fractions with Common Denominator 152

Multiply the numerator and denominator of 2/8 by 19, and multiply the numerator and denominator of 5/19 by 8 so both fractions share the common base 152.

2 × 19/8 × 19 = 38/152 and 5 × 8/19 × 8 = 40/152

Step 3

Add the Numerators

Now add the numerators (38 + 40 = 78) and keep the common denominator 152 unchanged.

38 + 40/152 = 78/152

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 78 and 152, which is 2. Divide both the numerator and denominator by 2.

78 ÷ 2/152 ÷ 2 = 39/76

Step 5

Decimal & Percentage Representation

Dividing the numerator 39 by denominator 76 produces a repeating decimal (approximately 0.513158, or 51.3158%).

39 ÷ 76 = 0.513158 (51.3158%)

Visual Representation

The diagram below illustrates 2/8 plus 5/19 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`39/76`
Mixed Number Form	`39/76`
Decimal Form	`0.513158`
Percentage	`51.3158%`

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Frequently Asked Questions

What is 2/8 plus 5/19 as a fraction?

2/8 + 5/19 in simplest fraction form is 39/76.

What is 2/8 plus 5/19 as a decimal?

2/8 + 5/19 converted to a decimal is 0.513158.

What is 2/8 plus 5/19 as a percentage?

2/8 + 5/19 expressed as a percentage is 51.3158%.

Does 2/8 plus 5/19 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.513158...) because the denominator contains prime factors other than 2 and 5.