What is 5/27 plus 2/9? (Answer: 11/27)

Exact Answer

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Problem: What is 5/27 plus 2/9?
Formula / Expression: 5/27 + 2/9
Final Answer: 11/27
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 27 is an exact multiple of 9 (9 × 3 = 27). The Least Common Denominator (LCD) is simply 27, meaning we only need to scale one fraction.
Working: LCD(27, 9) = 27

Step 2: Convert to Equivalent Fractions with Common Denominator 27
Multiply the numerator and denominator of 5/27 by 1, and multiply the numerator and denominator of 2/9 by 3 so both fractions share the common base 27.
Working: 5 × 1/27 × 1 = 5/27 and 2 × 3/9 × 3 = 6/27

Step 3: Add the Numerators
Now add the numerators (5 + 6 = 11) and keep the common denominator 27 unchanged.
Working: 5 + 6/27 = 11/27

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 11 and 27 is 1, confirming that 11/27 cannot be reduced further—it is already in its simplest irreducible form.
Working: 11/27

Step 5: Decimal & Percentage Representation
Dividing the numerator 11 by denominator 27 produces a repeating decimal (approximately 0.407407, or 40.7407%).
Working: 11 ÷ 27 = 0.407407 (40.7407%)

Key Values:
- Simplified Fraction: 11/27
- Mixed Number Form: 11/27
- Decimal Value: 0.407407
- Percentage: 40.7407%

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Solved with FractionsCalc:
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5/27 + 2/9 = 11/27

Simplified Fraction

11/27

Mixed Number

Proper (11/27)

Decimal Value

0.407407

Percentage

40.7407%

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Step-by-Step Solution: 5/27 + 2/9

Step 1

Find the Least Common Denominator (LCD)

Notice that 27 is an exact multiple of 9 (9 × 3 = 27). The Least Common Denominator (LCD) is simply 27, meaning we only need to scale one fraction.

LCD(27, 9) = 27

Step 2

Convert to Equivalent Fractions with Common Denominator 27

Multiply the numerator and denominator of 5/27 by 1, and multiply the numerator and denominator of 2/9 by 3 so both fractions share the common base 27.

5 × 1/27 × 1 = 5/27 and 2 × 3/9 × 3 = 6/27

Step 3

Add the Numerators

Now add the numerators (5 + 6 = 11) and keep the common denominator 27 unchanged.

5 + 6/27 = 11/27

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 11 and 27 is 1, confirming that 11/27 cannot be reduced further—it is already in its simplest irreducible form.

11/27

Step 5

Decimal & Percentage Representation

Dividing the numerator 11 by denominator 27 produces a repeating decimal (approximately 0.407407, or 40.7407%).

11 ÷ 27 = 0.407407 (40.7407%)

Visual Representation

The diagram below illustrates 5/27 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`11/27`
Mixed Number Form	`11/27`
Decimal Form	`0.407407`
Percentage	`40.7407%`

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Frequently Asked Questions

What is 5/27 plus 2/9 as a fraction?

5/27 + 2/9 in simplest fraction form is 11/27.

What is 5/27 plus 2/9 as a decimal?

5/27 + 2/9 converted to a decimal is 0.407407.

What is 5/27 plus 2/9 as a percentage?

5/27 + 2/9 expressed as a percentage is 40.7407%.

Does 5/27 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.407407...) because the denominator contains prime factors other than 2 and 5.