What is 2/27 plus 2/4? (Answer: 31/54)

Exact Answer

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Problem: What is 2/27 plus 2/4?
Formula / Expression: 2/27 + 2/4
Final Answer: 31/54
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 27 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 27 × 4 = 108.
Working: LCD(27, 4) = 108

Step 2: Convert to Equivalent Fractions with Common Denominator 108
Multiply the numerator and denominator of 2/27 by 4, and multiply the numerator and denominator of 2/4 by 27 so both fractions share the common base 108.
Working: 2 × 4/27 × 4 = 8/108 and 2 × 27/4 × 27 = 54/108

Step 3: Add the Numerators
Now add the numerators (8 + 54 = 62) and keep the common denominator 108 unchanged.
Working: 8 + 54/108 = 62/108

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 62 and 108, which is 2. Divide both the numerator and denominator by 2.
Working: 62 ÷ 2/108 ÷ 2 = 31/54

Step 5: Decimal & Percentage Representation
Dividing the numerator 31 by denominator 54 produces a repeating decimal (approximately 0.574074, or 57.4074%).
Working: 31 ÷ 54 = 0.574074 (57.4074%)

Key Values:
- Simplified Fraction: 31/54
- Mixed Number Form: 31/54
- Decimal Value: 0.574074
- Percentage: 57.4074%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-27-plus-2-4/
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2/27 + 2/4 = 31/54

Simplified Fraction

31/54

Mixed Number

Proper (31/54)

Decimal Value

0.574074

Percentage

57.4074%

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Step-by-Step Solution: 2/27 + 2/4

Step 1

Find the Least Common Denominator (LCD)

The denominators 27 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 27 × 4 = 108.

LCD(27, 4) = 108

Step 2

Convert to Equivalent Fractions with Common Denominator 108

Multiply the numerator and denominator of 2/27 by 4, and multiply the numerator and denominator of 2/4 by 27 so both fractions share the common base 108.

2 × 4/27 × 4 = 8/108 and 2 × 27/4 × 27 = 54/108

Step 3

Add the Numerators

Now add the numerators (8 + 54 = 62) and keep the common denominator 108 unchanged.

8 + 54/108 = 62/108

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 62 and 108, which is 2. Divide both the numerator and denominator by 2.

62 ÷ 2/108 ÷ 2 = 31/54

Step 5

Decimal & Percentage Representation

Dividing the numerator 31 by denominator 54 produces a repeating decimal (approximately 0.574074, or 57.4074%).

31 ÷ 54 = 0.574074 (57.4074%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`31/54`
Mixed Number Form	`31/54`
Decimal Form	`0.574074`
Percentage	`57.4074%`

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Frequently Asked Questions

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

2/27 + 2/4 in simplest fraction form is 31/54.

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

2/27 + 2/4 converted to a decimal is 0.574074.

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

2/27 + 2/4 expressed as a percentage is 57.4074%.

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

It results in a repeating decimal (approximately 0.574074...) because the denominator contains prime factors other than 2 and 5.