What is 8/38 plus 2/9? (Answer: 74/171)

Exact Answer

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Problem: What is 8/38 plus 2/9?
Formula / Expression: 8/38 + 2/9
Final Answer: 74/171
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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 8/38 by 9, and multiply the numerator and denominator of 2/9 by 38 so both fractions share the common base 342.
Working: 8 × 9/38 × 9 = 72/342 and 2 × 38/9 × 38 = 76/342

Step 3: Add the Numerators
Now add the numerators (72 + 76 = 148) and keep the common denominator 342 unchanged.
Working: 72 + 76/342 = 148/342

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 148 and 342, which is 2. Divide both the numerator and denominator by 2.
Working: 148 ÷ 2/342 ÷ 2 = 74/171

Step 5: Decimal & Percentage Representation
Dividing the numerator 74 by denominator 171 produces a repeating decimal (approximately 0.432749, or 43.2749%).
Working: 74 ÷ 171 = 0.432749 (43.2749%)

Key Values:
- Simplified Fraction: 74/171
- Mixed Number Form: 74/171
- Decimal Value: 0.432749
- Percentage: 43.2749%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-8-38-plus-2-9/
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8/38 + 2/9 = 74/171

Simplified Fraction

74/171

Mixed Number

Proper (74/171)

Decimal Value

0.432749

Percentage

43.2749%

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Step-by-Step Solution: 8/38 + 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 8/38 by 9, and multiply the numerator and denominator of 2/9 by 38 so both fractions share the common base 342.

8 × 9/38 × 9 = 72/342 and 2 × 38/9 × 38 = 76/342

Step 3

Add the Numerators

Now add the numerators (72 + 76 = 148) and keep the common denominator 342 unchanged.

72 + 76/342 = 148/342

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 148 and 342, which is 2. Divide both the numerator and denominator by 2.

148 ÷ 2/342 ÷ 2 = 74/171

Step 5

Decimal & Percentage Representation

Dividing the numerator 74 by denominator 171 produces a repeating decimal (approximately 0.432749, or 43.2749%).

74 ÷ 171 = 0.432749 (43.2749%)

Visual Representation

The diagram below illustrates 8/38 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`74/171`
Mixed Number Form	`74/171`
Decimal Form	`0.432749`
Percentage	`43.2749%`

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Frequently Asked Questions

What is 8/38 plus 2/9 as a fraction?

8/38 + 2/9 in simplest fraction form is 74/171.

What is 8/38 plus 2/9 as a decimal?

8/38 + 2/9 converted to a decimal is 0.432749.

What is 8/38 plus 2/9 as a percentage?

8/38 + 2/9 expressed as a percentage is 43.2749%.

Does 8/38 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.432749...) because the denominator contains prime factors other than 2 and 5.