What is 2/9 plus 9/38? (Answer: 157/342)

Exact Answer

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Problem: What is 2/9 plus 9/38?
Formula / Expression: 2/9 + 9/38
Final Answer: 157/342
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 342
Multiply the numerator and denominator of 2/9 by 38, and multiply the numerator and denominator of 9/38 by 9 so both fractions share the common base 342.
Working: 2 × 38/9 × 38 = 76/342 and 9 × 9/38 × 9 = 81/342

Step 3: Add the Numerators
Now add the numerators (76 + 81 = 157) and keep the common denominator 342 unchanged.
Working: 76 + 81/342 = 157/342

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 157 and 342 is 1, confirming that 157/342 cannot be reduced further—it is already in its simplest irreducible form.
Working: 157/342

Step 5: Decimal & Percentage Representation
Dividing the numerator 157 by denominator 342 produces a repeating decimal (approximately 0.459064, or 45.9064%).
Working: 157 ÷ 342 = 0.459064 (45.9064%)

Key Values:
- Simplified Fraction: 157/342
- Mixed Number Form: 157/342
- Decimal Value: 0.459064
- Percentage: 45.9064%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-9-plus-9-38/
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2/9 + 9/38 = 157/342

Simplified Fraction

157/342

Mixed Number

Proper (157/342)

Decimal Value

0.459064

Percentage

45.9064%

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

Step 1

Find the Least Common Denominator (LCD)

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

LCD(9, 38) = 342

Step 2

Convert to Equivalent Fractions with Common Denominator 342

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

2 × 38/9 × 38 = 76/342 and 9 × 9/38 × 9 = 81/342

Step 3

Add the Numerators

Now add the numerators (76 + 81 = 157) and keep the common denominator 342 unchanged.

76 + 81/342 = 157/342

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 157 and 342 is 1, confirming that 157/342 cannot be reduced further—it is already in its simplest irreducible form.

157/342

Step 5

Decimal & Percentage Representation

Dividing the numerator 157 by denominator 342 produces a repeating decimal (approximately 0.459064, or 45.9064%).

157 ÷ 342 = 0.459064 (45.9064%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`157/342`
Mixed Number Form	`157/342`
Decimal Form	`0.459064`
Percentage	`45.9064%`

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Frequently Asked Questions

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

2/9 + 9/38 in simplest fraction form is 157/342.

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

2/9 + 9/38 converted to a decimal is 0.459064.

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

2/9 + 9/38 expressed as a percentage is 45.9064%.

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

It results in a repeating decimal (approximately 0.459064...) because the denominator contains prime factors other than 2 and 5.