What is 2/9 plus 5/19? (Answer: 83/171)

Exact Answer

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Problem: What is 2/9 plus 5/19?
Formula / Expression: 2/9 + 5/19
Final Answer: 83/171
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 19 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 19 = 171.
Working: LCD(9, 19) = 171

Step 2: Convert to Equivalent Fractions with Common Denominator 171
Multiply the numerator and denominator of 2/9 by 19, and multiply the numerator and denominator of 5/19 by 9 so both fractions share the common base 171.
Working: 2 × 19/9 × 19 = 38/171 and 5 × 9/19 × 9 = 45/171

Step 3: Add the Numerators
Now add the numerators (38 + 45 = 83) and keep the common denominator 171 unchanged.
Working: 38 + 45/171 = 83/171

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 83 and 171 is 1, confirming that 83/171 cannot be reduced further—it is already in its simplest irreducible form.
Working: 83/171

Step 5: Decimal & Percentage Representation
Dividing the numerator 83 by denominator 171 produces a repeating decimal (approximately 0.48538, or 48.538%).
Working: 83 ÷ 171 = 0.48538 (48.538%)

Key Values:
- Simplified Fraction: 83/171
- Mixed Number Form: 83/171
- Decimal Value: 0.48538
- Percentage: 48.538%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-9-plus-5-19/
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2/9 + 5/19 = 83/171

Simplified Fraction

83/171

Mixed Number

Proper (83/171)

Decimal Value

0.48538

Percentage

48.538%

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Step-by-Step Solution: 2/9 + 5/19

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 19 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 19 = 171.

LCD(9, 19) = 171

Step 2

Convert to Equivalent Fractions with Common Denominator 171

Multiply the numerator and denominator of 2/9 by 19, and multiply the numerator and denominator of 5/19 by 9 so both fractions share the common base 171.

2 × 19/9 × 19 = 38/171 and 5 × 9/19 × 9 = 45/171

Step 3

Add the Numerators

Now add the numerators (38 + 45 = 83) and keep the common denominator 171 unchanged.

38 + 45/171 = 83/171

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 83 and 171 is 1, confirming that 83/171 cannot be reduced further—it is already in its simplest irreducible form.

83/171

Step 5

Decimal & Percentage Representation

Dividing the numerator 83 by denominator 171 produces a repeating decimal (approximately 0.48538, or 48.538%).

83 ÷ 171 = 0.48538 (48.538%)

Visual Representation

The diagram below illustrates 2/9 plus 5/19 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`83/171`
Mixed Number Form	`83/171`
Decimal Form	`0.48538`
Percentage	`48.538%`

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Frequently Asked Questions

What is 2/9 plus 5/19 as a fraction?

2/9 + 5/19 in simplest fraction form is 83/171.

What is 2/9 plus 5/19 as a decimal?

2/9 + 5/19 converted to a decimal is 0.48538.

What is 2/9 plus 5/19 as a percentage?

2/9 + 5/19 expressed as a percentage is 48.538%.

Does 2/9 plus 5/19 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.48538...) because the denominator contains prime factors other than 2 and 5.