What is 2/9 plus 9/31? (Answer: 143/279)

Exact Answer

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Problem: What is 2/9 plus 9/31?
Formula / Expression: 2/9 + 9/31
Final Answer: 143/279
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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 9/31 by 9 so both fractions share the common base 279.
Working: 2 × 31/9 × 31 = 62/279 and 9 × 9/31 × 9 = 81/279

Step 3: Add the Numerators
Now add the numerators (62 + 81 = 143) and keep the common denominator 279 unchanged.
Working: 62 + 81/279 = 143/279

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 143 and 279 is 1, confirming that 143/279 cannot be reduced further—it is already in its simplest irreducible form.
Working: 143/279

Step 5: Decimal & Percentage Representation
Dividing the numerator 143 by denominator 279 produces a repeating decimal (approximately 0.512545, or 51.2545%).
Working: 143 ÷ 279 = 0.512545 (51.2545%)

Key Values:
- Simplified Fraction: 143/279
- Mixed Number Form: 143/279
- Decimal Value: 0.512545
- Percentage: 51.2545%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-9-plus-9-31/
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2/9 + 9/31 = 143/279

Simplified Fraction

143/279

Mixed Number

Proper (143/279)

Decimal Value

0.512545

Percentage

51.2545%

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

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 9/31 by 9 so both fractions share the common base 279.

2 × 31/9 × 31 = 62/279 and 9 × 9/31 × 9 = 81/279

Step 3

Add the Numerators

Now add the numerators (62 + 81 = 143) and keep the common denominator 279 unchanged.

62 + 81/279 = 143/279

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 143 and 279 is 1, confirming that 143/279 cannot be reduced further—it is already in its simplest irreducible form.

143/279

Step 5

Decimal & Percentage Representation

Dividing the numerator 143 by denominator 279 produces a repeating decimal (approximately 0.512545, or 51.2545%).

143 ÷ 279 = 0.512545 (51.2545%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`143/279`
Mixed Number Form	`143/279`
Decimal Form	`0.512545`
Percentage	`51.2545%`

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Frequently Asked Questions

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

2/9 + 9/31 in simplest fraction form is 143/279.

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

2/9 + 9/31 converted to a decimal is 0.512545.

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

2/9 + 9/31 expressed as a percentage is 51.2545%.

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

It results in a repeating decimal (approximately 0.512545...) because the denominator contains prime factors other than 2 and 5.