What is 2/8 plus 7/27? (Answer: 55/108)

Exact Answer

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Problem: What is 2/8 plus 7/27?
Formula / Expression: 2/8 + 7/27
Final Answer: 55/108
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 8 and 27 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 8 × 27 = 216.
Working: LCD(8, 27) = 216

Step 2: Convert to Equivalent Fractions with Common Denominator 216
Multiply the numerator and denominator of 2/8 by 27, and multiply the numerator and denominator of 7/27 by 8 so both fractions share the common base 216.
Working: 2 × 27/8 × 27 = 54/216 and 7 × 8/27 × 8 = 56/216

Step 3: Add the Numerators
Now add the numerators (54 + 56 = 110) and keep the common denominator 216 unchanged.
Working: 54 + 56/216 = 110/216

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 110 and 216, which is 2. Divide both the numerator and denominator by 2.
Working: 110 ÷ 2/216 ÷ 2 = 55/108

Step 5: Decimal & Percentage Representation
Dividing the numerator 55 by denominator 108 produces a repeating decimal (approximately 0.509259, or 50.9259%).
Working: 55 ÷ 108 = 0.509259 (50.9259%)

Key Values:
- Simplified Fraction: 55/108
- Mixed Number Form: 55/108
- Decimal Value: 0.509259
- Percentage: 50.9259%

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Solved with FractionsCalc:
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2/8 + 7/27 = 55/108

Simplified Fraction

55/108

Mixed Number

Proper (55/108)

Decimal Value

0.509259

Percentage

50.9259%

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Step-by-Step Solution: 2/8 + 7/27

Step 1

Find the Least Common Denominator (LCD)

The denominators 8 and 27 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 8 × 27 = 216.

LCD(8, 27) = 216

Step 2

Convert to Equivalent Fractions with Common Denominator 216

Multiply the numerator and denominator of 2/8 by 27, and multiply the numerator and denominator of 7/27 by 8 so both fractions share the common base 216.

2 × 27/8 × 27 = 54/216 and 7 × 8/27 × 8 = 56/216

Step 3

Add the Numerators

Now add the numerators (54 + 56 = 110) and keep the common denominator 216 unchanged.

54 + 56/216 = 110/216

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 110 and 216, which is 2. Divide both the numerator and denominator by 2.

110 ÷ 2/216 ÷ 2 = 55/108

Step 5

Decimal & Percentage Representation

Dividing the numerator 55 by denominator 108 produces a repeating decimal (approximately 0.509259, or 50.9259%).

55 ÷ 108 = 0.509259 (50.9259%)

Visual Representation

The diagram below illustrates 2/8 plus 7/27 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`55/108`
Mixed Number Form	`55/108`
Decimal Form	`0.509259`
Percentage	`50.9259%`

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Frequently Asked Questions

What is 2/8 plus 7/27 as a fraction?

2/8 + 7/27 in simplest fraction form is 55/108.

What is 2/8 plus 7/27 as a decimal?

2/8 + 7/27 converted to a decimal is 0.509259.

What is 2/8 plus 7/27 as a percentage?

2/8 + 7/27 expressed as a percentage is 50.9259%.

Does 2/8 plus 7/27 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.509259...) because the denominator contains prime factors other than 2 and 5.