What is 2/9 plus 8/31? (Answer: 134/279)

Exact Answer

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Problem: What is 2/9 plus 8/31?
Formula / Expression: 2/9 + 8/31
Final Answer: 134/279
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 31 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 31 = 279.
Working: LCD(9, 31) = 279

Step 2: Convert to Equivalent Fractions with Common Denominator 279
Multiply the numerator and denominator of 2/9 by 31, and multiply the numerator and denominator of 8/31 by 9 so both fractions share the common base 279.
Working: 2 × 31/9 × 31 = 62/279 and 8 × 9/31 × 9 = 72/279

Step 3: Add the Numerators
Now add the numerators (62 + 72 = 134) and keep the common denominator 279 unchanged.
Working: 62 + 72/279 = 134/279

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 134 and 279 is 1, confirming that 134/279 cannot be reduced further—it is already in its simplest irreducible form.
Working: 134/279

Step 5: Decimal & Percentage Representation
Dividing the numerator 134 by denominator 279 produces a repeating decimal (approximately 0.480287, or 48.0287%).
Working: 134 ÷ 279 = 0.480287 (48.0287%)

Key Values:
- Simplified Fraction: 134/279
- Mixed Number Form: 134/279
- Decimal Value: 0.480287
- Percentage: 48.0287%

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Solved with FractionsCalc:
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2/9 + 8/31 = 134/279

Simplified Fraction

134/279

Mixed Number

Proper (134/279)

Decimal Value

0.480287

Percentage

48.0287%

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Step-by-Step Solution: 2/9 + 8/31

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 31 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 31 = 279.

LCD(9, 31) = 279

Step 2

Convert to Equivalent Fractions with Common Denominator 279

Multiply the numerator and denominator of 2/9 by 31, and multiply the numerator and denominator of 8/31 by 9 so both fractions share the common base 279.

2 × 31/9 × 31 = 62/279 and 8 × 9/31 × 9 = 72/279

Step 3

Add the Numerators

Now add the numerators (62 + 72 = 134) and keep the common denominator 279 unchanged.

62 + 72/279 = 134/279

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 134 and 279 is 1, confirming that 134/279 cannot be reduced further—it is already in its simplest irreducible form.

134/279

Step 5

Decimal & Percentage Representation

Dividing the numerator 134 by denominator 279 produces a repeating decimal (approximately 0.480287, or 48.0287%).

134 ÷ 279 = 0.480287 (48.0287%)

Visual Representation

The diagram below illustrates 2/9 plus 8/31 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`134/279`
Mixed Number Form	`134/279`
Decimal Form	`0.480287`
Percentage	`48.0287%`

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Frequently Asked Questions

What is 2/9 plus 8/31 as a fraction?

2/9 + 8/31 in simplest fraction form is 134/279.

What is 2/9 plus 8/31 as a decimal?

2/9 + 8/31 converted to a decimal is 0.480287.

What is 2/9 plus 8/31 as a percentage?

2/9 + 8/31 expressed as a percentage is 48.0287%.

Does 2/9 plus 8/31 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.480287...) because the denominator contains prime factors other than 2 and 5.