What is 2/19 plus 3/9? (Answer: 25/57)

Exact Answer

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Problem: What is 2/19 plus 3/9?
Formula / Expression: 2/19 + 3/9
Final Answer: 25/57
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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 2/19 by 9, and multiply the numerator and denominator of 3/9 by 19 so both fractions share the common base 171.
Working: 2 × 9/19 × 9 = 18/171 and 3 × 19/9 × 19 = 57/171

Step 3: Add the Numerators
Now add the numerators (18 + 57 = 75) and keep the common denominator 171 unchanged.
Working: 18 + 57/171 = 75/171

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 75 and 171, which is 3. Divide both the numerator and denominator by 3.
Working: 75 ÷ 3/171 ÷ 3 = 25/57

Step 5: Decimal & Percentage Representation
Dividing the numerator 25 by denominator 57 produces a repeating decimal (approximately 0.438596, or 43.8596%).
Working: 25 ÷ 57 = 0.438596 (43.8596%)

Key Values:
- Simplified Fraction: 25/57
- Mixed Number Form: 25/57
- Decimal Value: 0.438596
- Percentage: 43.8596%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-19-plus-3-9/
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2/19 + 3/9 = 25/57

Simplified Fraction

25/57

Mixed Number

Proper (25/57)

Decimal Value

0.438596

Percentage

43.8596%

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Step-by-Step Solution: 2/19 + 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 2/19 by 9, and multiply the numerator and denominator of 3/9 by 19 so both fractions share the common base 171.

2 × 9/19 × 9 = 18/171 and 3 × 19/9 × 19 = 57/171

Step 3

Add the Numerators

Now add the numerators (18 + 57 = 75) and keep the common denominator 171 unchanged.

18 + 57/171 = 75/171

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 75 and 171, which is 3. Divide both the numerator and denominator by 3.

75 ÷ 3/171 ÷ 3 = 25/57

Step 5

Decimal & Percentage Representation

Dividing the numerator 25 by denominator 57 produces a repeating decimal (approximately 0.438596, or 43.8596%).

25 ÷ 57 = 0.438596 (43.8596%)

Visual Representation

The diagram below illustrates 2/19 plus 3/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`25/57`
Mixed Number Form	`25/57`
Decimal Form	`0.438596`
Percentage	`43.8596%`

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Frequently Asked Questions

What is 2/19 plus 3/9 as a fraction?

2/19 + 3/9 in simplest fraction form is 25/57.

What is 2/19 plus 3/9 as a decimal?

2/19 + 3/9 converted to a decimal is 0.438596.

What is 2/19 plus 3/9 as a percentage?

2/19 + 3/9 expressed as a percentage is 43.8596%.

Does 2/19 plus 3/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.438596...) because the denominator contains prime factors other than 2 and 5.