What is 5/19 plus 2/5? (Answer: 63/95)

Exact Answer

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Problem: What is 5/19 plus 2/5?
Formula / Expression: 5/19 + 2/5
Final Answer: 63/95
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 19 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 19 × 5 = 95.
Working: LCD(19, 5) = 95

Step 2: Convert to Equivalent Fractions with Common Denominator 95
Multiply the numerator and denominator of 5/19 by 5, and multiply the numerator and denominator of 2/5 by 19 so both fractions share the common base 95.
Working: 5 × 5/19 × 5 = 25/95 and 2 × 19/5 × 19 = 38/95

Step 3: Add the Numerators
Now add the numerators (25 + 38 = 63) and keep the common denominator 95 unchanged.
Working: 25 + 38/95 = 63/95

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 63 and 95 is 1, confirming that 63/95 cannot be reduced further—it is already in its simplest irreducible form.
Working: 63/95

Step 5: Decimal & Percentage Representation
Dividing the numerator 63 by denominator 95 produces a repeating decimal (approximately 0.663158, or 66.3158%).
Working: 63 ÷ 95 = 0.663158 (66.3158%)

Key Values:
- Simplified Fraction: 63/95
- Mixed Number Form: 63/95
- Decimal Value: 0.663158
- Percentage: 66.3158%

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Solved with FractionsCalc:
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5/19 + 2/5 = 63/95

Simplified Fraction

63/95

Mixed Number

Proper (63/95)

Decimal Value

0.663158

Percentage

66.3158%

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

Step 1

Find the Least Common Denominator (LCD)

The denominators 19 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 19 × 5 = 95.

LCD(19, 5) = 95

Step 2

Convert to Equivalent Fractions with Common Denominator 95

Multiply the numerator and denominator of 5/19 by 5, and multiply the numerator and denominator of 2/5 by 19 so both fractions share the common base 95.

5 × 5/19 × 5 = 25/95 and 2 × 19/5 × 19 = 38/95

Step 3

Add the Numerators

Now add the numerators (25 + 38 = 63) and keep the common denominator 95 unchanged.

25 + 38/95 = 63/95

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 63 and 95 is 1, confirming that 63/95 cannot be reduced further—it is already in its simplest irreducible form.

63/95

Step 5

Decimal & Percentage Representation

Dividing the numerator 63 by denominator 95 produces a repeating decimal (approximately 0.663158, or 66.3158%).

63 ÷ 95 = 0.663158 (66.3158%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`63/95`
Mixed Number Form	`63/95`
Decimal Form	`0.663158`
Percentage	`66.3158%`

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Frequently Asked Questions

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

5/19 + 2/5 in simplest fraction form is 63/95.

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

5/19 + 2/5 converted to a decimal is 0.663158.

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

5/19 + 2/5 expressed as a percentage is 66.3158%.

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

It results in a repeating decimal (approximately 0.663158...) because the denominator contains prime factors other than 2 and 5.