What is 2/27 plus 2/8? (Answer: 35/108)

Exact Answer

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Problem: What is 2/27 plus 2/8?
Formula / Expression: 2/27 + 2/8
Final Answer: 35/108
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 216
Multiply the numerator and denominator of 2/27 by 8, and multiply the numerator and denominator of 2/8 by 27 so both fractions share the common base 216.
Working: 2 × 8/27 × 8 = 16/216 and 2 × 27/8 × 27 = 54/216

Step 3: Add the Numerators
Now add the numerators (16 + 54 = 70) and keep the common denominator 216 unchanged.
Working: 16 + 54/216 = 70/216

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 70 and 216, which is 2. Divide both the numerator and denominator by 2.
Working: 70 ÷ 2/216 ÷ 2 = 35/108

Step 5: Decimal & Percentage Representation
Dividing the numerator 35 by denominator 108 produces a repeating decimal (approximately 0.324074, or 32.4074%).
Working: 35 ÷ 108 = 0.324074 (32.4074%)

Key Values:
- Simplified Fraction: 35/108
- Mixed Number Form: 35/108
- Decimal Value: 0.324074
- Percentage: 32.4074%

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Solved with FractionsCalc:
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2/27 + 2/8 = 35/108

Simplified Fraction

35/108

Mixed Number

Proper (35/108)

Decimal Value

0.324074

Percentage

32.4074%

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

Step 1

Find the Least Common Denominator (LCD)

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

LCD(27, 8) = 216

Step 2

Convert to Equivalent Fractions with Common Denominator 216

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

2 × 8/27 × 8 = 16/216 and 2 × 27/8 × 27 = 54/216

Step 3

Add the Numerators

Now add the numerators (16 + 54 = 70) and keep the common denominator 216 unchanged.

16 + 54/216 = 70/216

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 70 and 216, which is 2. Divide both the numerator and denominator by 2.

70 ÷ 2/216 ÷ 2 = 35/108

Step 5

Decimal & Percentage Representation

Dividing the numerator 35 by denominator 108 produces a repeating decimal (approximately 0.324074, or 32.4074%).

35 ÷ 108 = 0.324074 (32.4074%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`35/108`
Mixed Number Form	`35/108`
Decimal Form	`0.324074`
Percentage	`32.4074%`

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Frequently Asked Questions

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

2/27 + 2/8 in simplest fraction form is 35/108.

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

2/27 + 2/8 converted to a decimal is 0.324074.

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

2/27 + 2/8 expressed as a percentage is 32.4074%.

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

It results in a repeating decimal (approximately 0.324074...) because the denominator contains prime factors other than 2 and 5.