What is 2/7 plus 9/31? (Answer: 125/217)

Exact Answer

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Problem: What is 2/7 plus 9/31?
Formula / Expression: 2/7 + 9/31
Final Answer: 125/217
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 7 and 31 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 31 = 217.
Working: LCD(7, 31) = 217

Step 2: Convert to Equivalent Fractions with Common Denominator 217
Multiply the numerator and denominator of 2/7 by 31, and multiply the numerator and denominator of 9/31 by 7 so both fractions share the common base 217.
Working: 2 × 31/7 × 31 = 62/217 and 9 × 7/31 × 7 = 63/217

Step 3: Add the Numerators
Now add the numerators (62 + 63 = 125) and keep the common denominator 217 unchanged.
Working: 62 + 63/217 = 125/217

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 125 and 217 is 1, confirming that 125/217 cannot be reduced further—it is already in its simplest irreducible form.
Working: 125/217

Step 5: Decimal & Percentage Representation
Dividing the numerator 125 by denominator 217 produces a repeating decimal (approximately 0.576037, or 57.6037%).
Working: 125 ÷ 217 = 0.576037 (57.6037%)

Key Values:
- Simplified Fraction: 125/217
- Mixed Number Form: 125/217
- Decimal Value: 0.576037
- Percentage: 57.6037%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-7-plus-9-31/
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2/7 + 9/31 = 125/217

Simplified Fraction

125/217

Mixed Number

Proper (125/217)

Decimal Value

0.576037

Percentage

57.6037%

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Step-by-Step Solution: 2/7 + 9/31

Step 1

Find the Least Common Denominator (LCD)

The denominators 7 and 31 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 31 = 217.

LCD(7, 31) = 217

Step 2

Convert to Equivalent Fractions with Common Denominator 217

Multiply the numerator and denominator of 2/7 by 31, and multiply the numerator and denominator of 9/31 by 7 so both fractions share the common base 217.

2 × 31/7 × 31 = 62/217 and 9 × 7/31 × 7 = 63/217

Step 3

Add the Numerators

Now add the numerators (62 + 63 = 125) and keep the common denominator 217 unchanged.

62 + 63/217 = 125/217

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 125 and 217 is 1, confirming that 125/217 cannot be reduced further—it is already in its simplest irreducible form.

125/217

Step 5

Decimal & Percentage Representation

Dividing the numerator 125 by denominator 217 produces a repeating decimal (approximately 0.576037, or 57.6037%).

125 ÷ 217 = 0.576037 (57.6037%)

Visual Representation

The diagram below illustrates 2/7 plus 9/31 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`125/217`
Mixed Number Form	`125/217`
Decimal Form	`0.576037`
Percentage	`57.6037%`

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Frequently Asked Questions

What is 2/7 plus 9/31 as a fraction?

2/7 + 9/31 in simplest fraction form is 125/217.

What is 2/7 plus 9/31 as a decimal?

2/7 + 9/31 converted to a decimal is 0.576037.

What is 2/7 plus 9/31 as a percentage?

2/7 + 9/31 expressed as a percentage is 57.6037%.

Does 2/7 plus 9/31 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.576037...) because the denominator contains prime factors other than 2 and 5.