What is 3/13 plus 5/19? (Answer: 122/247)

Exact Answer

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Problem: What is 3/13 plus 5/19?
Formula / Expression: 3/13 + 5/19
Final Answer: 122/247
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 13 and 19 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 19 = 247.
Working: LCD(13, 19) = 247

Step 2: Convert to Equivalent Fractions with Common Denominator 247
Multiply the numerator and denominator of 3/13 by 19, and multiply the numerator and denominator of 5/19 by 13 so both fractions share the common base 247.
Working: 3 × 19/13 × 19 = 57/247 and 5 × 13/19 × 13 = 65/247

Step 3: Add the Numerators
Now add the numerators (57 + 65 = 122) and keep the common denominator 247 unchanged.
Working: 57 + 65/247 = 122/247

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 122 and 247 is 1, confirming that 122/247 cannot be reduced further—it is already in its simplest irreducible form.
Working: 122/247

Step 5: Decimal & Percentage Representation
Dividing the numerator 122 by denominator 247 produces a repeating decimal (approximately 0.493927, or 49.3927%).
Working: 122 ÷ 247 = 0.493927 (49.3927%)

Key Values:
- Simplified Fraction: 122/247
- Mixed Number Form: 122/247
- Decimal Value: 0.493927
- Percentage: 49.3927%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-13-plus-5-19/
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3/13 + 5/19 = 122/247

Simplified Fraction

122/247

Mixed Number

Proper (122/247)

Decimal Value

0.493927

Percentage

49.3927%

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Step-by-Step Solution: 3/13 + 5/19

Step 1

Find the Least Common Denominator (LCD)

The denominators 13 and 19 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 19 = 247.

LCD(13, 19) = 247

Step 2

Convert to Equivalent Fractions with Common Denominator 247

Multiply the numerator and denominator of 3/13 by 19, and multiply the numerator and denominator of 5/19 by 13 so both fractions share the common base 247.

3 × 19/13 × 19 = 57/247 and 5 × 13/19 × 13 = 65/247

Step 3

Add the Numerators

Now add the numerators (57 + 65 = 122) and keep the common denominator 247 unchanged.

57 + 65/247 = 122/247

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 122 and 247 is 1, confirming that 122/247 cannot be reduced further—it is already in its simplest irreducible form.

122/247

Step 5

Decimal & Percentage Representation

Dividing the numerator 122 by denominator 247 produces a repeating decimal (approximately 0.493927, or 49.3927%).

122 ÷ 247 = 0.493927 (49.3927%)

Visual Representation

The diagram below illustrates 3/13 plus 5/19 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`122/247`
Mixed Number Form	`122/247`
Decimal Form	`0.493927`
Percentage	`49.3927%`

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Frequently Asked Questions

What is 3/13 plus 5/19 as a fraction?

3/13 + 5/19 in simplest fraction form is 122/247.

What is 3/13 plus 5/19 as a decimal?

3/13 + 5/19 converted to a decimal is 0.493927.

What is 3/13 plus 5/19 as a percentage?

3/13 + 5/19 expressed as a percentage is 49.3927%.

Does 3/13 plus 5/19 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.493927...) because the denominator contains prime factors other than 2 and 5.