What is 3/27 plus 2/4? (Answer: 11/18)

Exact Answer

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Problem: What is 3/27 plus 2/4?
Formula / Expression: 3/27 + 2/4
Final Answer: 11/18
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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 3/27 by 4, and multiply the numerator and denominator of 2/4 by 27 so both fractions share the common base 108.
Working: 3 × 4/27 × 4 = 12/108 and 2 × 27/4 × 27 = 54/108

Step 3: Add the Numerators
Now add the numerators (12 + 54 = 66) and keep the common denominator 108 unchanged.
Working: 12 + 54/108 = 66/108

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 66 and 108, which is 6. Divide both the numerator and denominator by 6.
Working: 66 ÷ 6/108 ÷ 6 = 11/18

Step 5: Decimal & Percentage Representation
Dividing the numerator 11 by denominator 18 produces a repeating decimal (approximately 0.611111, or 61.1111%).
Working: 11 ÷ 18 = 0.611111 (61.1111%)

Key Values:
- Simplified Fraction: 11/18
- Mixed Number Form: 11/18
- Decimal Value: 0.611111
- Percentage: 61.1111%

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Solved with FractionsCalc:
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3/27 + 2/4 = 11/18

Simplified Fraction

11/18

Mixed Number

Proper (11/18)

Decimal Value

0.611111

Percentage

61.1111%

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Step-by-Step Solution: 3/27 + 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 3/27 by 4, and multiply the numerator and denominator of 2/4 by 27 so both fractions share the common base 108.

3 × 4/27 × 4 = 12/108 and 2 × 27/4 × 27 = 54/108

Step 3

Add the Numerators

Now add the numerators (12 + 54 = 66) and keep the common denominator 108 unchanged.

12 + 54/108 = 66/108

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 66 and 108, which is 6. Divide both the numerator and denominator by 6.

66 ÷ 6/108 ÷ 6 = 11/18

Step 5

Decimal & Percentage Representation

Dividing the numerator 11 by denominator 18 produces a repeating decimal (approximately 0.611111, or 61.1111%).

11 ÷ 18 = 0.611111 (61.1111%)

Visual Representation

The diagram below illustrates 3/27 plus 2/4 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`11/18`
Mixed Number Form	`11/18`
Decimal Form	`0.611111`
Percentage	`61.1111%`

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Frequently Asked Questions

What is 3/27 plus 2/4 as a fraction?

3/27 + 2/4 in simplest fraction form is 11/18.

What is 3/27 plus 2/4 as a decimal?

3/27 + 2/4 converted to a decimal is 0.611111.

What is 3/27 plus 2/4 as a percentage?

3/27 + 2/4 expressed as a percentage is 61.1111%.

Does 3/27 plus 2/4 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.611111...) because the denominator contains prime factors other than 2 and 5.