What is 5/19 plus 3/9? (Answer: 34/57)

Exact Answer

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Problem: What is 5/19 plus 3/9?
Formula / Expression: 5/19 + 3/9
Final Answer: 34/57
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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 5/19 by 9, and multiply the numerator and denominator of 3/9 by 19 so both fractions share the common base 171.
Working: 5 × 9/19 × 9 = 45/171 and 3 × 19/9 × 19 = 57/171

Step 3: Add the Numerators
Now add the numerators (45 + 57 = 102) and keep the common denominator 171 unchanged.
Working: 45 + 57/171 = 102/171

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 102 and 171, which is 3. Divide both the numerator and denominator by 3.
Working: 102 ÷ 3/171 ÷ 3 = 34/57

Step 5: Decimal & Percentage Representation
Dividing the numerator 34 by denominator 57 produces a repeating decimal (approximately 0.596491, or 59.6491%).
Working: 34 ÷ 57 = 0.596491 (59.6491%)

Key Values:
- Simplified Fraction: 34/57
- Mixed Number Form: 34/57
- Decimal Value: 0.596491
- Percentage: 59.6491%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-19-plus-3-9/
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5/19 + 3/9 = 34/57

Simplified Fraction

34/57

Mixed Number

Proper (34/57)

Decimal Value

0.596491

Percentage

59.6491%

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

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

5 × 9/19 × 9 = 45/171 and 3 × 19/9 × 19 = 57/171

Step 3

Add the Numerators

Now add the numerators (45 + 57 = 102) and keep the common denominator 171 unchanged.

45 + 57/171 = 102/171

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 102 and 171, which is 3. Divide both the numerator and denominator by 3.

102 ÷ 3/171 ÷ 3 = 34/57

Step 5

Decimal & Percentage Representation

Dividing the numerator 34 by denominator 57 produces a repeating decimal (approximately 0.596491, or 59.6491%).

34 ÷ 57 = 0.596491 (59.6491%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`34/57`
Mixed Number Form	`34/57`
Decimal Form	`0.596491`
Percentage	`59.6491%`

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Frequently Asked Questions

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

5/19 + 3/9 in simplest fraction form is 34/57.

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

5/19 + 3/9 converted to a decimal is 0.596491.

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

5/19 + 3/9 expressed as a percentage is 59.6491%.

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

It results in a repeating decimal (approximately 0.596491...) because the denominator contains prime factors other than 2 and 5.