What is 2/9 plus 7/27? (Answer: 13/27)

Exact Answer

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Problem: What is 2/9 plus 7/27?
Formula / Expression: 2/9 + 7/27
Final Answer: 13/27
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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(9, 27) = 27

Step 2: Convert to Equivalent Fractions with Common Denominator 27
Multiply the numerator and denominator of 2/9 by 3, and multiply the numerator and denominator of 7/27 by 1 so both fractions share the common base 27.
Working: 2 × 3/9 × 3 = 6/27 and 7 × 1/27 × 1 = 7/27

Step 3: Add the Numerators
Now add the numerators (6 + 7 = 13) and keep the common denominator 27 unchanged.
Working: 6 + 7/27 = 13/27

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 13 and 27 is 1, confirming that 13/27 cannot be reduced further—it is already in its simplest irreducible form.
Working: 13/27

Step 5: Decimal & Percentage Representation
Dividing the numerator 13 by denominator 27 produces a repeating decimal (approximately 0.481481, or 48.1481%).
Working: 13 ÷ 27 = 0.481481 (48.1481%)

Key Values:
- Simplified Fraction: 13/27
- Mixed Number Form: 13/27
- Decimal Value: 0.481481
- Percentage: 48.1481%

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Solved with FractionsCalc:
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2/9 + 7/27 = 13/27

Simplified Fraction

13/27

Mixed Number

Proper (13/27)

Decimal Value

0.481481

Percentage

48.1481%

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Step-by-Step Solution: 2/9 + 7/27

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(9, 27) = 27

Step 2

Convert to Equivalent Fractions with Common Denominator 27

Multiply the numerator and denominator of 2/9 by 3, and multiply the numerator and denominator of 7/27 by 1 so both fractions share the common base 27.

2 × 3/9 × 3 = 6/27 and 7 × 1/27 × 1 = 7/27

Step 3

Add the Numerators

Now add the numerators (6 + 7 = 13) and keep the common denominator 27 unchanged.

6 + 7/27 = 13/27

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 13 and 27 is 1, confirming that 13/27 cannot be reduced further—it is already in its simplest irreducible form.

13/27

Step 5

Decimal & Percentage Representation

Dividing the numerator 13 by denominator 27 produces a repeating decimal (approximately 0.481481, or 48.1481%).

13 ÷ 27 = 0.481481 (48.1481%)

Visual Representation

The diagram below illustrates 2/9 plus 7/27 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`13/27`
Mixed Number Form	`13/27`
Decimal Form	`0.481481`
Percentage	`48.1481%`

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Frequently Asked Questions

What is 2/9 plus 7/27 as a fraction?

2/9 + 7/27 in simplest fraction form is 13/27.

What is 2/9 plus 7/27 as a decimal?

2/9 + 7/27 converted to a decimal is 0.481481.

What is 2/9 plus 7/27 as a percentage?

2/9 + 7/27 expressed as a percentage is 48.1481%.

Does 2/9 plus 7/27 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.481481...) because the denominator contains prime factors other than 2 and 5.