What is 4/31 plus 2/3? (Answer: 74/93)

Exact Answer

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Problem: What is 4/31 plus 2/3?
Formula / Expression: 4/31 + 2/3
Final Answer: 74/93
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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 4/31 by 3, and multiply the numerator and denominator of 2/3 by 31 so both fractions share the common base 93.
Working: 4 × 3/31 × 3 = 12/93 and 2 × 31/3 × 31 = 62/93

Step 3: Add the Numerators
Now add the numerators (12 + 62 = 74) and keep the common denominator 93 unchanged.
Working: 12 + 62/93 = 74/93

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 74 and 93 is 1, confirming that 74/93 cannot be reduced further—it is already in its simplest irreducible form.
Working: 74/93

Step 5: Decimal & Percentage Representation
Dividing the numerator 74 by denominator 93 produces a repeating decimal (approximately 0.795699, or 79.5699%).
Working: 74 ÷ 93 = 0.795699 (79.5699%)

Key Values:
- Simplified Fraction: 74/93
- Mixed Number Form: 74/93
- Decimal Value: 0.795699
- Percentage: 79.5699%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-31-plus-2-3/
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4/31 + 2/3 = 74/93

Simplified Fraction

74/93

Mixed Number

Proper (74/93)

Decimal Value

0.795699

Percentage

79.5699%

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Step-by-Step Solution: 4/31 + 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 4/31 by 3, and multiply the numerator and denominator of 2/3 by 31 so both fractions share the common base 93.

4 × 3/31 × 3 = 12/93 and 2 × 31/3 × 31 = 62/93

Step 3

Add the Numerators

Now add the numerators (12 + 62 = 74) and keep the common denominator 93 unchanged.

12 + 62/93 = 74/93

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 74 and 93 is 1, confirming that 74/93 cannot be reduced further—it is already in its simplest irreducible form.

74/93

Step 5

Decimal & Percentage Representation

Dividing the numerator 74 by denominator 93 produces a repeating decimal (approximately 0.795699, or 79.5699%).

74 ÷ 93 = 0.795699 (79.5699%)

Visual Representation

The diagram below illustrates 4/31 plus 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`74/93`
Mixed Number Form	`74/93`
Decimal Form	`0.795699`
Percentage	`79.5699%`

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Frequently Asked Questions

What is 4/31 plus 2/3 as a fraction?

4/31 + 2/3 in simplest fraction form is 74/93.

What is 4/31 plus 2/3 as a decimal?

4/31 + 2/3 converted to a decimal is 0.795699.

What is 4/31 plus 2/3 as a percentage?

4/31 + 2/3 expressed as a percentage is 79.5699%.

Does 4/31 plus 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.795699...) because the denominator contains prime factors other than 2 and 5.