What is 9/38 plus 2/3? (Answer: 103/114)

Exact Answer

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Problem: What is 9/38 plus 2/3?
Formula / Expression: 9/38 + 2/3
Final Answer: 103/114
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 38 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 38 × 3 = 114.
Working: LCD(38, 3) = 114

Step 2: Convert to Equivalent Fractions with Common Denominator 114
Multiply the numerator and denominator of 9/38 by 3, and multiply the numerator and denominator of 2/3 by 38 so both fractions share the common base 114.
Working: 9 × 3/38 × 3 = 27/114 and 2 × 38/3 × 38 = 76/114

Step 3: Add the Numerators
Now add the numerators (27 + 76 = 103) and keep the common denominator 114 unchanged.
Working: 27 + 76/114 = 103/114

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 103 and 114 is 1, confirming that 103/114 cannot be reduced further—it is already in its simplest irreducible form.
Working: 103/114

Step 5: Decimal & Percentage Representation
Dividing the numerator 103 by denominator 114 produces a repeating decimal (approximately 0.903509, or 90.3509%).
Working: 103 ÷ 114 = 0.903509 (90.3509%)

Key Values:
- Simplified Fraction: 103/114
- Mixed Number Form: 103/114
- Decimal Value: 0.903509
- Percentage: 90.3509%

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Solved with FractionsCalc:
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9/38 + 2/3 = 103/114

Simplified Fraction

103/114

Mixed Number

Proper (103/114)

Decimal Value

0.903509

Percentage

90.3509%

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

Step 1

Find the Least Common Denominator (LCD)

The denominators 38 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 38 × 3 = 114.

LCD(38, 3) = 114

Step 2

Convert to Equivalent Fractions with Common Denominator 114

Multiply the numerator and denominator of 9/38 by 3, and multiply the numerator and denominator of 2/3 by 38 so both fractions share the common base 114.

9 × 3/38 × 3 = 27/114 and 2 × 38/3 × 38 = 76/114

Step 3

Add the Numerators

Now add the numerators (27 + 76 = 103) and keep the common denominator 114 unchanged.

27 + 76/114 = 103/114

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 103 and 114 is 1, confirming that 103/114 cannot be reduced further—it is already in its simplest irreducible form.

103/114

Step 5

Decimal & Percentage Representation

Dividing the numerator 103 by denominator 114 produces a repeating decimal (approximately 0.903509, or 90.3509%).

103 ÷ 114 = 0.903509 (90.3509%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`103/114`
Mixed Number Form	`103/114`
Decimal Form	`0.903509`
Percentage	`90.3509%`

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Frequently Asked Questions

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

9/38 + 2/3 in simplest fraction form is 103/114.

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

9/38 + 2/3 converted to a decimal is 0.903509.

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

9/38 + 2/3 expressed as a percentage is 90.3509%.

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

It results in a repeating decimal (approximately 0.903509...) because the denominator contains prime factors other than 2 and 5.