What is 3/31 plus 2/9? (Answer: 89/279)

Exact Answer

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Problem: What is 3/31 plus 2/9?
Formula / Expression: 3/31 + 2/9
Final Answer: 89/279
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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 3/31 by 9, and multiply the numerator and denominator of 2/9 by 31 so both fractions share the common base 279.
Working: 3 × 9/31 × 9 = 27/279 and 2 × 31/9 × 31 = 62/279

Step 3: Add the Numerators
Now add the numerators (27 + 62 = 89) and keep the common denominator 279 unchanged.
Working: 27 + 62/279 = 89/279

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 89 and 279 is 1, confirming that 89/279 cannot be reduced further—it is already in its simplest irreducible form.
Working: 89/279

Step 5: Decimal & Percentage Representation
Dividing the numerator 89 by denominator 279 produces a repeating decimal (approximately 0.318996, or 31.8996%).
Working: 89 ÷ 279 = 0.318996 (31.8996%)

Key Values:
- Simplified Fraction: 89/279
- Mixed Number Form: 89/279
- Decimal Value: 0.318996
- Percentage: 31.8996%

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Solved with FractionsCalc:
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3/31 + 2/9 = 89/279

Simplified Fraction

89/279

Mixed Number

Proper (89/279)

Decimal Value

0.318996

Percentage

31.8996%

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Step-by-Step Solution: 3/31 + 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 3/31 by 9, and multiply the numerator and denominator of 2/9 by 31 so both fractions share the common base 279.

3 × 9/31 × 9 = 27/279 and 2 × 31/9 × 31 = 62/279

Step 3

Add the Numerators

Now add the numerators (27 + 62 = 89) and keep the common denominator 279 unchanged.

27 + 62/279 = 89/279

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 89 and 279 is 1, confirming that 89/279 cannot be reduced further—it is already in its simplest irreducible form.

89/279

Step 5

Decimal & Percentage Representation

Dividing the numerator 89 by denominator 279 produces a repeating decimal (approximately 0.318996, or 31.8996%).

89 ÷ 279 = 0.318996 (31.8996%)

Visual Representation

The diagram below illustrates 3/31 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`89/279`
Mixed Number Form	`89/279`
Decimal Form	`0.318996`
Percentage	`31.8996%`

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Frequently Asked Questions

What is 3/31 plus 2/9 as a fraction?

3/31 + 2/9 in simplest fraction form is 89/279.

What is 3/31 plus 2/9 as a decimal?

3/31 + 2/9 converted to a decimal is 0.318996.

What is 3/31 plus 2/9 as a percentage?

3/31 + 2/9 expressed as a percentage is 31.8996%.

Does 3/31 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.318996...) because the denominator contains prime factors other than 2 and 5.