What is 5/19 plus 2/6? (Answer: 34/57)

Exact Answer

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Problem: What is 5/19 plus 2/6?
Formula / Expression: 5/19 + 2/6
Final Answer: 34/57
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 19 and 6 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 19 × 6 = 114.
Working: LCD(19, 6) = 114

Step 2: Convert to Equivalent Fractions with Common Denominator 114
Multiply the numerator and denominator of 5/19 by 6, and multiply the numerator and denominator of 2/6 by 19 so both fractions share the common base 114.
Working: 5 × 6/19 × 6 = 30/114 and 2 × 19/6 × 19 = 38/114

Step 3: Add the Numerators
Now add the numerators (30 + 38 = 68) and keep the common denominator 114 unchanged.
Working: 30 + 38/114 = 68/114

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 68 and 114, which is 2. Divide both the numerator and denominator by 2.
Working: 68 ÷ 2/114 ÷ 2 = 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-2-6/
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5/19 + 2/6 = 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 + 2/6

Step 1

Find the Least Common Denominator (LCD)

The denominators 19 and 6 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 19 × 6 = 114.

LCD(19, 6) = 114

Step 2

Convert to Equivalent Fractions with Common Denominator 114

Multiply the numerator and denominator of 5/19 by 6, and multiply the numerator and denominator of 2/6 by 19 so both fractions share the common base 114.

5 × 6/19 × 6 = 30/114 and 2 × 19/6 × 19 = 38/114

Step 3

Add the Numerators

Now add the numerators (30 + 38 = 68) and keep the common denominator 114 unchanged.

30 + 38/114 = 68/114

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 68 and 114, which is 2. Divide both the numerator and denominator by 2.

68 ÷ 2/114 ÷ 2 = 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 2/6 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 2/6 as a fraction?

5/19 + 2/6 in simplest fraction form is 34/57.

What is 5/19 plus 2/6 as a decimal?

5/19 + 2/6 converted to a decimal is 0.596491.

What is 5/19 plus 2/6 as a percentage?

5/19 + 2/6 expressed as a percentage is 59.6491%.

Does 5/19 plus 2/6 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.