What is 3/19 plus 5/9? (Answer: 122/171)

Exact Answer

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Problem: What is 3/19 plus 5/9?
Formula / Expression: 3/19 + 5/9
Final Answer: 122/171
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 171
Multiply the numerator and denominator of 3/19 by 9, and multiply the numerator and denominator of 5/9 by 19 so both fractions share the common base 171.
Working: 3 × 9/19 × 9 = 27/171 and 5 × 19/9 × 19 = 95/171

Step 3: Add the Numerators
Now add the numerators (27 + 95 = 122) and keep the common denominator 171 unchanged.
Working: 27 + 95/171 = 122/171

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 122 and 171 is 1, confirming that 122/171 cannot be reduced further—it is already in its simplest irreducible form.
Working: 122/171

Step 5: Decimal & Percentage Representation
Dividing the numerator 122 by denominator 171 produces a repeating decimal (approximately 0.71345, or 71.345%).
Working: 122 ÷ 171 = 0.71345 (71.345%)

Key Values:
- Simplified Fraction: 122/171
- Mixed Number Form: 122/171
- Decimal Value: 0.71345
- Percentage: 71.345%

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Solved with FractionsCalc:
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3/19 + 5/9 = 122/171

Simplified Fraction

122/171

Mixed Number

Proper (122/171)

Decimal Value

0.71345

Percentage

71.345%

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Step-by-Step Solution: 3/19 + 5/9

Step 1

Find the Least Common Denominator (LCD)

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

LCD(19, 9) = 171

Step 2

Convert to Equivalent Fractions with Common Denominator 171

Multiply the numerator and denominator of 3/19 by 9, and multiply the numerator and denominator of 5/9 by 19 so both fractions share the common base 171.

3 × 9/19 × 9 = 27/171 and 5 × 19/9 × 19 = 95/171

Step 3

Add the Numerators

Now add the numerators (27 + 95 = 122) and keep the common denominator 171 unchanged.

27 + 95/171 = 122/171

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 122 and 171 is 1, confirming that 122/171 cannot be reduced further—it is already in its simplest irreducible form.

122/171

Step 5

Decimal & Percentage Representation

Dividing the numerator 122 by denominator 171 produces a repeating decimal (approximately 0.71345, or 71.345%).

122 ÷ 171 = 0.71345 (71.345%)

Visual Representation

The diagram below illustrates 3/19 plus 5/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`122/171`
Mixed Number Form	`122/171`
Decimal Form	`0.71345`
Percentage	`71.345%`

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Frequently Asked Questions

What is 3/19 plus 5/9 as a fraction?

3/19 + 5/9 in simplest fraction form is 122/171.

What is 3/19 plus 5/9 as a decimal?

3/19 + 5/9 converted to a decimal is 0.71345.

What is 3/19 plus 5/9 as a percentage?

3/19 + 5/9 expressed as a percentage is 71.345%.

Does 3/19 plus 5/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.71345...) because the denominator contains prime factors other than 2 and 5.