What is 3/31 plus 2/8? (Answer: 43/124)

Exact Answer

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Problem: What is 3/31 plus 2/8?
Formula / Expression: 3/31 + 2/8
Final Answer: 43/124
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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 3/31 by 8, and multiply the numerator and denominator of 2/8 by 31 so both fractions share the common base 248.
Working: 3 × 8/31 × 8 = 24/248 and 2 × 31/8 × 31 = 62/248

Step 3: Add the Numerators
Now add the numerators (24 + 62 = 86) and keep the common denominator 248 unchanged.
Working: 24 + 62/248 = 86/248

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 86 and 248, which is 2. Divide both the numerator and denominator by 2.
Working: 86 ÷ 2/248 ÷ 2 = 43/124

Step 5: Decimal & Percentage Representation
Dividing the numerator 43 by denominator 124 produces a repeating decimal (approximately 0.346774, or 34.6774%).
Working: 43 ÷ 124 = 0.346774 (34.6774%)

Key Values:
- Simplified Fraction: 43/124
- Mixed Number Form: 43/124
- Decimal Value: 0.346774
- Percentage: 34.6774%

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Solved with FractionsCalc:
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3/31 + 2/8 = 43/124

Simplified Fraction

43/124

Mixed Number

Proper (43/124)

Decimal Value

0.346774

Percentage

34.6774%

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Step-by-Step Solution: 3/31 + 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 3/31 by 8, and multiply the numerator and denominator of 2/8 by 31 so both fractions share the common base 248.

3 × 8/31 × 8 = 24/248 and 2 × 31/8 × 31 = 62/248

Step 3

Add the Numerators

Now add the numerators (24 + 62 = 86) and keep the common denominator 248 unchanged.

24 + 62/248 = 86/248

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 86 and 248, which is 2. Divide both the numerator and denominator by 2.

86 ÷ 2/248 ÷ 2 = 43/124

Step 5

Decimal & Percentage Representation

Dividing the numerator 43 by denominator 124 produces a repeating decimal (approximately 0.346774, or 34.6774%).

43 ÷ 124 = 0.346774 (34.6774%)

Visual Representation

The diagram below illustrates 3/31 plus 2/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`43/124`
Mixed Number Form	`43/124`
Decimal Form	`0.346774`
Percentage	`34.6774%`

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Frequently Asked Questions

What is 3/31 plus 2/8 as a fraction?

3/31 + 2/8 in simplest fraction form is 43/124.

What is 3/31 plus 2/8 as a decimal?

3/31 + 2/8 converted to a decimal is 0.346774.

What is 3/31 plus 2/8 as a percentage?

3/31 + 2/8 expressed as a percentage is 34.6774%.

Does 3/31 plus 2/8 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.346774...) because the denominator contains prime factors other than 2 and 5.