What is 5/38 plus 2/9? (Answer: 121/342)

Exact Answer

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Problem: What is 5/38 plus 2/9?
Formula / Expression: 5/38 + 2/9
Final Answer: 121/342
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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 5/38 by 9, and multiply the numerator and denominator of 2/9 by 38 so both fractions share the common base 342.
Working: 5 × 9/38 × 9 = 45/342 and 2 × 38/9 × 38 = 76/342

Step 3: Add the Numerators
Now add the numerators (45 + 76 = 121) and keep the common denominator 342 unchanged.
Working: 45 + 76/342 = 121/342

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 121 and 342 is 1, confirming that 121/342 cannot be reduced further—it is already in its simplest irreducible form.
Working: 121/342

Step 5: Decimal & Percentage Representation
Dividing the numerator 121 by denominator 342 produces a repeating decimal (approximately 0.353801, or 35.3801%).
Working: 121 ÷ 342 = 0.353801 (35.3801%)

Key Values:
- Simplified Fraction: 121/342
- Mixed Number Form: 121/342
- Decimal Value: 0.353801
- Percentage: 35.3801%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-38-plus-2-9/
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5/38 + 2/9 = 121/342

Simplified Fraction

121/342

Mixed Number

Proper (121/342)

Decimal Value

0.353801

Percentage

35.3801%

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Step-by-Step Solution: 5/38 + 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 5/38 by 9, and multiply the numerator and denominator of 2/9 by 38 so both fractions share the common base 342.

5 × 9/38 × 9 = 45/342 and 2 × 38/9 × 38 = 76/342

Step 3

Add the Numerators

Now add the numerators (45 + 76 = 121) and keep the common denominator 342 unchanged.

45 + 76/342 = 121/342

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 121 and 342 is 1, confirming that 121/342 cannot be reduced further—it is already in its simplest irreducible form.

121/342

Step 5

Decimal & Percentage Representation

Dividing the numerator 121 by denominator 342 produces a repeating decimal (approximately 0.353801, or 35.3801%).

121 ÷ 342 = 0.353801 (35.3801%)

Visual Representation

The diagram below illustrates 5/38 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`121/342`
Mixed Number Form	`121/342`
Decimal Form	`0.353801`
Percentage	`35.3801%`

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Frequently Asked Questions

What is 5/38 plus 2/9 as a fraction?

5/38 + 2/9 in simplest fraction form is 121/342.

What is 5/38 plus 2/9 as a decimal?

5/38 + 2/9 converted to a decimal is 0.353801.

What is 5/38 plus 2/9 as a percentage?

5/38 + 2/9 expressed as a percentage is 35.3801%.

Does 5/38 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.353801...) because the denominator contains prime factors other than 2 and 5.