What is 3/31 plus 2/7? (Answer: 83/217)

Exact Answer

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Problem: What is 3/31 plus 2/7?
Formula / Expression: 3/31 + 2/7
Final Answer: 83/217
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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 3/31 by 7, and multiply the numerator and denominator of 2/7 by 31 so both fractions share the common base 217.
Working: 3 × 7/31 × 7 = 21/217 and 2 × 31/7 × 31 = 62/217

Step 3: Add the Numerators
Now add the numerators (21 + 62 = 83) and keep the common denominator 217 unchanged.
Working: 21 + 62/217 = 83/217

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 83 and 217 is 1, confirming that 83/217 cannot be reduced further—it is already in its simplest irreducible form.
Working: 83/217

Step 5: Decimal & Percentage Representation
Dividing the numerator 83 by denominator 217 produces a repeating decimal (approximately 0.382488, or 38.2488%).
Working: 83 ÷ 217 = 0.382488 (38.2488%)

Key Values:
- Simplified Fraction: 83/217
- Mixed Number Form: 83/217
- Decimal Value: 0.382488
- Percentage: 38.2488%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-31-plus-2-7/
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3/31 + 2/7 = 83/217

Simplified Fraction

83/217

Mixed Number

Proper (83/217)

Decimal Value

0.382488

Percentage

38.2488%

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Step-by-Step Solution: 3/31 + 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 3/31 by 7, and multiply the numerator and denominator of 2/7 by 31 so both fractions share the common base 217.

3 × 7/31 × 7 = 21/217 and 2 × 31/7 × 31 = 62/217

Step 3

Add the Numerators

Now add the numerators (21 + 62 = 83) and keep the common denominator 217 unchanged.

21 + 62/217 = 83/217

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 83 and 217 is 1, confirming that 83/217 cannot be reduced further—it is already in its simplest irreducible form.

83/217

Step 5

Decimal & Percentage Representation

Dividing the numerator 83 by denominator 217 produces a repeating decimal (approximately 0.382488, or 38.2488%).

83 ÷ 217 = 0.382488 (38.2488%)

Visual Representation

The diagram below illustrates 3/31 plus 2/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`83/217`
Mixed Number Form	`83/217`
Decimal Form	`0.382488`
Percentage	`38.2488%`

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Frequently Asked Questions

What is 3/31 plus 2/7 as a fraction?

3/31 + 2/7 in simplest fraction form is 83/217.

What is 3/31 plus 2/7 as a decimal?

3/31 + 2/7 converted to a decimal is 0.382488.

What is 3/31 plus 2/7 as a percentage?

3/31 + 2/7 expressed as a percentage is 38.2488%.

Does 3/31 plus 2/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.382488...) because the denominator contains prime factors other than 2 and 5.