What is 5/31 plus 2/9? (Answer: 107/279)

Exact Answer

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Problem: What is 5/31 plus 2/9?
Formula / Expression: 5/31 + 2/9
Final Answer: 107/279
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 279
Multiply the numerator and denominator of 5/31 by 9, and multiply the numerator and denominator of 2/9 by 31 so both fractions share the common base 279.
Working: 5 × 9/31 × 9 = 45/279 and 2 × 31/9 × 31 = 62/279

Step 3: Add the Numerators
Now add the numerators (45 + 62 = 107) and keep the common denominator 279 unchanged.
Working: 45 + 62/279 = 107/279

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 107 and 279 is 1, confirming that 107/279 cannot be reduced further—it is already in its simplest irreducible form.
Working: 107/279

Step 5: Decimal & Percentage Representation
Dividing the numerator 107 by denominator 279 produces a repeating decimal (approximately 0.383513, or 38.3513%).
Working: 107 ÷ 279 = 0.383513 (38.3513%)

Key Values:
- Simplified Fraction: 107/279
- Mixed Number Form: 107/279
- Decimal Value: 0.383513
- Percentage: 38.3513%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-31-plus-2-9/
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5/31 + 2/9 = 107/279

Simplified Fraction

107/279

Mixed Number

Proper (107/279)

Decimal Value

0.383513

Percentage

38.3513%

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Step-by-Step Solution: 5/31 + 2/9

Step 1

Find the Least Common Denominator (LCD)

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

LCD(31, 9) = 279

Step 2

Convert to Equivalent Fractions with Common Denominator 279

Multiply the numerator and denominator of 5/31 by 9, and multiply the numerator and denominator of 2/9 by 31 so both fractions share the common base 279.

5 × 9/31 × 9 = 45/279 and 2 × 31/9 × 31 = 62/279

Step 3

Add the Numerators

Now add the numerators (45 + 62 = 107) and keep the common denominator 279 unchanged.

45 + 62/279 = 107/279

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 107 and 279 is 1, confirming that 107/279 cannot be reduced further—it is already in its simplest irreducible form.

107/279

Step 5

Decimal & Percentage Representation

Dividing the numerator 107 by denominator 279 produces a repeating decimal (approximately 0.383513, or 38.3513%).

107 ÷ 279 = 0.383513 (38.3513%)

Visual Representation

The diagram below illustrates 5/31 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`107/279`
Mixed Number Form	`107/279`
Decimal Form	`0.383513`
Percentage	`38.3513%`

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Frequently Asked Questions

What is 5/31 plus 2/9 as a fraction?

5/31 + 2/9 in simplest fraction form is 107/279.

What is 5/31 plus 2/9 as a decimal?

5/31 + 2/9 converted to a decimal is 0.383513.

What is 5/31 plus 2/9 as a percentage?

5/31 + 2/9 expressed as a percentage is 38.3513%.

Does 5/31 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.383513...) because the denominator contains prime factors other than 2 and 5.