What is 2/8 plus 9/31? (Answer: 67/124)

Exact Answer

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Problem: What is 2/8 plus 9/31?
Formula / Expression: 2/8 + 9/31
Final Answer: 67/124
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 248
Multiply the numerator and denominator of 2/8 by 31, and multiply the numerator and denominator of 9/31 by 8 so both fractions share the common base 248.
Working: 2 × 31/8 × 31 = 62/248 and 9 × 8/31 × 8 = 72/248

Step 3: Add the Numerators
Now add the numerators (62 + 72 = 134) and keep the common denominator 248 unchanged.
Working: 62 + 72/248 = 134/248

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 134 and 248, which is 2. Divide both the numerator and denominator by 2.
Working: 134 ÷ 2/248 ÷ 2 = 67/124

Step 5: Decimal & Percentage Representation
Dividing the numerator 67 by denominator 124 produces a repeating decimal (approximately 0.540323, or 54.0323%).
Working: 67 ÷ 124 = 0.540323 (54.0323%)

Key Values:
- Simplified Fraction: 67/124
- Mixed Number Form: 67/124
- Decimal Value: 0.540323
- Percentage: 54.0323%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-8-plus-9-31/
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2/8 + 9/31 = 67/124

Simplified Fraction

67/124

Mixed Number

Proper (67/124)

Decimal Value

0.540323

Percentage

54.0323%

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Step-by-Step Solution: 2/8 + 9/31

Step 1

Find the Least Common Denominator (LCD)

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

LCD(8, 31) = 248

Step 2

Convert to Equivalent Fractions with Common Denominator 248

Multiply the numerator and denominator of 2/8 by 31, and multiply the numerator and denominator of 9/31 by 8 so both fractions share the common base 248.

2 × 31/8 × 31 = 62/248 and 9 × 8/31 × 8 = 72/248

Step 3

Add the Numerators

Now add the numerators (62 + 72 = 134) and keep the common denominator 248 unchanged.

62 + 72/248 = 134/248

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 134 and 248, which is 2. Divide both the numerator and denominator by 2.

134 ÷ 2/248 ÷ 2 = 67/124

Step 5

Decimal & Percentage Representation

Dividing the numerator 67 by denominator 124 produces a repeating decimal (approximately 0.540323, or 54.0323%).

67 ÷ 124 = 0.540323 (54.0323%)

Visual Representation

The diagram below illustrates 2/8 plus 9/31 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`67/124`
Mixed Number Form	`67/124`
Decimal Form	`0.540323`
Percentage	`54.0323%`

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Frequently Asked Questions

What is 2/8 plus 9/31 as a fraction?

2/8 + 9/31 in simplest fraction form is 67/124.

What is 2/8 plus 9/31 as a decimal?

2/8 + 9/31 converted to a decimal is 0.540323.

What is 2/8 plus 9/31 as a percentage?

2/8 + 9/31 expressed as a percentage is 54.0323%.

Does 2/8 plus 9/31 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.540323...) because the denominator contains prime factors other than 2 and 5.