What is 3/38 plus 2/9? (Answer: 103/342)

Exact Answer

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Problem: What is 3/38 plus 2/9?
Formula / Expression: 3/38 + 2/9
Final Answer: 103/342
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 38 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 38 × 9 = 342.
Working: LCD(38, 9) = 342

Step 2: Convert to Equivalent Fractions with Common Denominator 342
Multiply the numerator and denominator of 3/38 by 9, and multiply the numerator and denominator of 2/9 by 38 so both fractions share the common base 342.
Working: 3 × 9/38 × 9 = 27/342 and 2 × 38/9 × 38 = 76/342

Step 3: Add the Numerators
Now add the numerators (27 + 76 = 103) and keep the common denominator 342 unchanged.
Working: 27 + 76/342 = 103/342

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 103 and 342 is 1, confirming that 103/342 cannot be reduced further—it is already in its simplest irreducible form.
Working: 103/342

Step 5: Decimal & Percentage Representation
Dividing the numerator 103 by denominator 342 produces a repeating decimal (approximately 0.30117, or 30.117%).
Working: 103 ÷ 342 = 0.30117 (30.117%)

Key Values:
- Simplified Fraction: 103/342
- Mixed Number Form: 103/342
- Decimal Value: 0.30117
- Percentage: 30.117%

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Solved with FractionsCalc:
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3/38 + 2/9 = 103/342

Simplified Fraction

103/342

Mixed Number

Proper (103/342)

Decimal Value

0.30117

Percentage

30.117%

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Step-by-Step Solution: 3/38 + 2/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 38 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 38 × 9 = 342.

LCD(38, 9) = 342

Step 2

Convert to Equivalent Fractions with Common Denominator 342

Multiply the numerator and denominator of 3/38 by 9, and multiply the numerator and denominator of 2/9 by 38 so both fractions share the common base 342.

3 × 9/38 × 9 = 27/342 and 2 × 38/9 × 38 = 76/342

Step 3

Add the Numerators

Now add the numerators (27 + 76 = 103) and keep the common denominator 342 unchanged.

27 + 76/342 = 103/342

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 103 and 342 is 1, confirming that 103/342 cannot be reduced further—it is already in its simplest irreducible form.

103/342

Step 5

Decimal & Percentage Representation

Dividing the numerator 103 by denominator 342 produces a repeating decimal (approximately 0.30117, or 30.117%).

103 ÷ 342 = 0.30117 (30.117%)

Visual Representation

The diagram below illustrates 3/38 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`103/342`
Mixed Number Form	`103/342`
Decimal Form	`0.30117`
Percentage	`30.117%`

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Frequently Asked Questions

What is 3/38 plus 2/9 as a fraction?

3/38 + 2/9 in simplest fraction form is 103/342.

What is 3/38 plus 2/9 as a decimal?

3/38 + 2/9 converted to a decimal is 0.30117.

What is 3/38 plus 2/9 as a percentage?

3/38 + 2/9 expressed as a percentage is 30.117%.

Does 3/38 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.30117...) because the denominator contains prime factors other than 2 and 5.