What is 2/31 plus 2/7? (Answer: 76/217)

Exact Answer

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Problem: What is 2/31 plus 2/7?
Formula / Expression: 2/31 + 2/7
Final Answer: 76/217
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 217
Multiply the numerator and denominator of 2/31 by 7, and multiply the numerator and denominator of 2/7 by 31 so both fractions share the common base 217.
Working: 2 × 7/31 × 7 = 14/217 and 2 × 31/7 × 31 = 62/217

Step 3: Add the Numerators
Now add the numerators (14 + 62 = 76) and keep the common denominator 217 unchanged.
Working: 14 + 62/217 = 76/217

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 76 and 217 is 1, confirming that 76/217 cannot be reduced further—it is already in its simplest irreducible form.
Working: 76/217

Step 5: Decimal & Percentage Representation
Dividing the numerator 76 by denominator 217 produces a repeating decimal (approximately 0.35023, or 35.023%).
Working: 76 ÷ 217 = 0.35023 (35.023%)

Key Values:
- Simplified Fraction: 76/217
- Mixed Number Form: 76/217
- Decimal Value: 0.35023
- Percentage: 35.023%

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Solved with FractionsCalc:
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2/31 + 2/7 = 76/217

Simplified Fraction

76/217

Mixed Number

Proper (76/217)

Decimal Value

0.35023

Percentage

35.023%

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

Step 1

Find the Least Common Denominator (LCD)

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

LCD(31, 7) = 217

Step 2

Convert to Equivalent Fractions with Common Denominator 217

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

2 × 7/31 × 7 = 14/217 and 2 × 31/7 × 31 = 62/217

Step 3

Add the Numerators

Now add the numerators (14 + 62 = 76) and keep the common denominator 217 unchanged.

14 + 62/217 = 76/217

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 76 and 217 is 1, confirming that 76/217 cannot be reduced further—it is already in its simplest irreducible form.

76/217

Step 5

Decimal & Percentage Representation

Dividing the numerator 76 by denominator 217 produces a repeating decimal (approximately 0.35023, or 35.023%).

76 ÷ 217 = 0.35023 (35.023%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`76/217`
Mixed Number Form	`76/217`
Decimal Form	`0.35023`
Percentage	`35.023%`

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Frequently Asked Questions

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

2/31 + 2/7 in simplest fraction form is 76/217.

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

2/31 + 2/7 converted to a decimal is 0.35023.

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

2/31 + 2/7 expressed as a percentage is 35.023%.

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

It results in a repeating decimal (approximately 0.35023...) because the denominator contains prime factors other than 2 and 5.