What is 3/31 plus 2/3? (Answer: 71/93)

Exact Answer

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Problem: What is 3/31 plus 2/3?
Formula / Expression: 3/31 + 2/3
Final Answer: 71/93
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 31 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 31 × 3 = 93.
Working: LCD(31, 3) = 93

Step 2: Convert to Equivalent Fractions with Common Denominator 93
Multiply the numerator and denominator of 3/31 by 3, and multiply the numerator and denominator of 2/3 by 31 so both fractions share the common base 93.
Working: 3 × 3/31 × 3 = 9/93 and 2 × 31/3 × 31 = 62/93

Step 3: Add the Numerators
Now add the numerators (9 + 62 = 71) and keep the common denominator 93 unchanged.
Working: 9 + 62/93 = 71/93

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 71 and 93 is 1, confirming that 71/93 cannot be reduced further—it is already in its simplest irreducible form.
Working: 71/93

Step 5: Decimal & Percentage Representation
Dividing the numerator 71 by denominator 93 produces a repeating decimal (approximately 0.763441, or 76.3441%).
Working: 71 ÷ 93 = 0.763441 (76.3441%)

Key Values:
- Simplified Fraction: 71/93
- Mixed Number Form: 71/93
- Decimal Value: 0.763441
- Percentage: 76.3441%

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Solved with FractionsCalc:
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3/31 + 2/3 = 71/93

Simplified Fraction

71/93

Mixed Number

Proper (71/93)

Decimal Value

0.763441

Percentage

76.3441%

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Step-by-Step Solution: 3/31 + 2/3

Step 1

Find the Least Common Denominator (LCD)

The denominators 31 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 31 × 3 = 93.

LCD(31, 3) = 93

Step 2

Convert to Equivalent Fractions with Common Denominator 93

Multiply the numerator and denominator of 3/31 by 3, and multiply the numerator and denominator of 2/3 by 31 so both fractions share the common base 93.

3 × 3/31 × 3 = 9/93 and 2 × 31/3 × 31 = 62/93

Step 3

Add the Numerators

Now add the numerators (9 + 62 = 71) and keep the common denominator 93 unchanged.

9 + 62/93 = 71/93

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 71 and 93 is 1, confirming that 71/93 cannot be reduced further—it is already in its simplest irreducible form.

71/93

Step 5

Decimal & Percentage Representation

Dividing the numerator 71 by denominator 93 produces a repeating decimal (approximately 0.763441, or 76.3441%).

71 ÷ 93 = 0.763441 (76.3441%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`71/93`
Mixed Number Form	`71/93`
Decimal Form	`0.763441`
Percentage	`76.3441%`

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Frequently Asked Questions

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

3/31 + 2/3 in simplest fraction form is 71/93.

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

3/31 + 2/3 converted to a decimal is 0.763441.

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

3/31 + 2/3 expressed as a percentage is 76.3441%.

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

It results in a repeating decimal (approximately 0.763441...) because the denominator contains prime factors other than 2 and 5.