What is 2/27 plus 2/12? (Answer: 13/54)

Exact Answer

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Problem: What is 2/27 plus 2/12?
Formula / Expression: 2/27 + 2/12
Final Answer: 13/54
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 27 and 12 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 108 (which is smaller than their product 27 × 12 = 324, keeping the calculation simpler).
Working: LCD(27, 12) = 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 2/12 by 9 so both fractions share the common base 108.
Working: 2 × 4/27 × 4 = 8/108 and 2 × 9/12 × 9 = 18/108

Step 3: Add the Numerators
Now add the numerators (8 + 18 = 26) and keep the common denominator 108 unchanged.
Working: 8 + 18/108 = 26/108

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 26 and 108, which is 2. Divide both the numerator and denominator by 2.
Working: 26 ÷ 2/108 ÷ 2 = 13/54

Step 5: Decimal & Percentage Representation
Dividing the numerator 13 by denominator 54 produces a repeating decimal (approximately 0.240741, or 24.0741%).
Working: 13 ÷ 54 = 0.240741 (24.0741%)

Key Values:
- Simplified Fraction: 13/54
- Mixed Number Form: 13/54
- Decimal Value: 0.240741
- Percentage: 24.0741%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-27-plus-2-12/
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2/27 + 2/12 = 13/54

Simplified Fraction

13/54

Mixed Number

Proper (13/54)

Decimal Value

0.240741

Percentage

24.0741%

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Step-by-Step Solution: 2/27 + 2/12

Step 1

Find the Least Common Denominator (LCD)

The denominators 27 and 12 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 108 (which is smaller than their product 27 × 12 = 324, keeping the calculation simpler).

LCD(27, 12) = 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 2/12 by 9 so both fractions share the common base 108.

2 × 4/27 × 4 = 8/108 and 2 × 9/12 × 9 = 18/108

Step 3

Add the Numerators

Now add the numerators (8 + 18 = 26) and keep the common denominator 108 unchanged.

8 + 18/108 = 26/108

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 26 and 108, which is 2. Divide both the numerator and denominator by 2.

26 ÷ 2/108 ÷ 2 = 13/54

Step 5

Decimal & Percentage Representation

Dividing the numerator 13 by denominator 54 produces a repeating decimal (approximately 0.240741, or 24.0741%).

13 ÷ 54 = 0.240741 (24.0741%)

Visual Representation

The diagram below illustrates 2/27 plus 2/12 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`13/54`
Mixed Number Form	`13/54`
Decimal Form	`0.240741`
Percentage	`24.0741%`

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Frequently Asked Questions

What is 2/27 plus 2/12 as a fraction?

2/27 + 2/12 in simplest fraction form is 13/54.

What is 2/27 plus 2/12 as a decimal?

2/27 + 2/12 converted to a decimal is 0.240741.

What is 2/27 plus 2/12 as a percentage?

2/27 + 2/12 expressed as a percentage is 24.0741%.

Does 2/27 plus 2/12 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.240741...) because the denominator contains prime factors other than 2 and 5.