What is 2/31 plus 2/8? (Answer: 39/124)

Exact Answer

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Problem: What is 2/31 plus 2/8?
Formula / Expression: 2/31 + 2/8
Final Answer: 39/124
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 31 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 31 × 8 = 248.
Working: LCD(31, 8) = 248

Step 2: Convert to Equivalent Fractions with Common Denominator 248
Multiply the numerator and denominator of 2/31 by 8, and multiply the numerator and denominator of 2/8 by 31 so both fractions share the common base 248.
Working: 2 × 8/31 × 8 = 16/248 and 2 × 31/8 × 31 = 62/248

Step 3: Add the Numerators
Now add the numerators (16 + 62 = 78) and keep the common denominator 248 unchanged.
Working: 16 + 62/248 = 78/248

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 78 and 248, which is 2. Divide both the numerator and denominator by 2.
Working: 78 ÷ 2/248 ÷ 2 = 39/124

Step 5: Decimal & Percentage Representation
Dividing the numerator 39 by denominator 124 produces a repeating decimal (approximately 0.314516, or 31.4516%).
Working: 39 ÷ 124 = 0.314516 (31.4516%)

Key Values:
- Simplified Fraction: 39/124
- Mixed Number Form: 39/124
- Decimal Value: 0.314516
- Percentage: 31.4516%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-31-plus-2-8/
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2/31 + 2/8 = 39/124

Simplified Fraction

39/124

Mixed Number

Proper (39/124)

Decimal Value

0.314516

Percentage

31.4516%

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Step-by-Step Solution: 2/31 + 2/8

Step 1

Find the Least Common Denominator (LCD)

The denominators 31 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 31 × 8 = 248.

LCD(31, 8) = 248

Step 2

Convert to Equivalent Fractions with Common Denominator 248

Multiply the numerator and denominator of 2/31 by 8, and multiply the numerator and denominator of 2/8 by 31 so both fractions share the common base 248.

2 × 8/31 × 8 = 16/248 and 2 × 31/8 × 31 = 62/248

Step 3

Add the Numerators

Now add the numerators (16 + 62 = 78) and keep the common denominator 248 unchanged.

16 + 62/248 = 78/248

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 78 and 248, which is 2. Divide both the numerator and denominator by 2.

78 ÷ 2/248 ÷ 2 = 39/124

Step 5

Decimal & Percentage Representation

Dividing the numerator 39 by denominator 124 produces a repeating decimal (approximately 0.314516, or 31.4516%).

39 ÷ 124 = 0.314516 (31.4516%)

Visual Representation

The diagram below illustrates 2/31 plus 2/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`39/124`
Mixed Number Form	`39/124`
Decimal Form	`0.314516`
Percentage	`31.4516%`

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Frequently Asked Questions

What is 2/31 plus 2/8 as a fraction?

2/31 + 2/8 in simplest fraction form is 39/124.

What is 2/31 plus 2/8 as a decimal?

2/31 + 2/8 converted to a decimal is 0.314516.

What is 2/31 plus 2/8 as a percentage?

2/31 + 2/8 expressed as a percentage is 31.4516%.

Does 2/31 plus 2/8 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.314516...) because the denominator contains prime factors other than 2 and 5.