What is 4/27 plus 2/8? (Answer: 43/108)

Exact Answer

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Problem: What is 4/27 plus 2/8?
Formula / Expression: 4/27 + 2/8
Final Answer: 43/108
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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 4/27 by 8, and multiply the numerator and denominator of 2/8 by 27 so both fractions share the common base 216.
Working: 4 × 8/27 × 8 = 32/216 and 2 × 27/8 × 27 = 54/216

Step 3: Add the Numerators
Now add the numerators (32 + 54 = 86) and keep the common denominator 216 unchanged.
Working: 32 + 54/216 = 86/216

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 86 and 216, which is 2. Divide both the numerator and denominator by 2.
Working: 86 ÷ 2/216 ÷ 2 = 43/108

Step 5: Decimal & Percentage Representation
Dividing the numerator 43 by denominator 108 produces a repeating decimal (approximately 0.398148, or 39.8148%).
Working: 43 ÷ 108 = 0.398148 (39.8148%)

Key Values:
- Simplified Fraction: 43/108
- Mixed Number Form: 43/108
- Decimal Value: 0.398148
- Percentage: 39.8148%

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Solved with FractionsCalc:
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4/27 + 2/8 = 43/108

Simplified Fraction

43/108

Mixed Number

Proper (43/108)

Decimal Value

0.398148

Percentage

39.8148%

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Step-by-Step Solution: 4/27 + 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 4/27 by 8, and multiply the numerator and denominator of 2/8 by 27 so both fractions share the common base 216.

4 × 8/27 × 8 = 32/216 and 2 × 27/8 × 27 = 54/216

Step 3

Add the Numerators

Now add the numerators (32 + 54 = 86) and keep the common denominator 216 unchanged.

32 + 54/216 = 86/216

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 86 and 216, which is 2. Divide both the numerator and denominator by 2.

86 ÷ 2/216 ÷ 2 = 43/108

Step 5

Decimal & Percentage Representation

Dividing the numerator 43 by denominator 108 produces a repeating decimal (approximately 0.398148, or 39.8148%).

43 ÷ 108 = 0.398148 (39.8148%)

Visual Representation

The diagram below illustrates 4/27 plus 2/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`43/108`
Mixed Number Form	`43/108`
Decimal Form	`0.398148`
Percentage	`39.8148%`

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Frequently Asked Questions

What is 4/27 plus 2/8 as a fraction?

4/27 + 2/8 in simplest fraction form is 43/108.

What is 4/27 plus 2/8 as a decimal?

4/27 + 2/8 converted to a decimal is 0.398148.

What is 4/27 plus 2/8 as a percentage?

4/27 + 2/8 expressed as a percentage is 39.8148%.

Does 4/27 plus 2/8 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.398148...) because the denominator contains prime factors other than 2 and 5.