What is 4/27 plus 2/9? (Answer: 10/27)

Exact Answer

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Problem: What is 4/27 plus 2/9?
Formula / Expression: 4/27 + 2/9
Final Answer: 10/27
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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 4/27 by 1, and multiply the numerator and denominator of 2/9 by 3 so both fractions share the common base 27.
Working: 4 × 1/27 × 1 = 4/27 and 2 × 3/9 × 3 = 6/27

Step 3: Add the Numerators
Now add the numerators (4 + 6 = 10) and keep the common denominator 27 unchanged.
Working: 4 + 6/27 = 10/27

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 10 and 27 is 1, confirming that 10/27 cannot be reduced further—it is already in its simplest irreducible form.
Working: 10/27

Step 5: Decimal & Percentage Representation
Dividing the numerator 10 by denominator 27 produces a repeating decimal (approximately 0.37037, or 37.037%).
Working: 10 ÷ 27 = 0.37037 (37.037%)

Key Values:
- Simplified Fraction: 10/27
- Mixed Number Form: 10/27
- Decimal Value: 0.37037
- Percentage: 37.037%

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Solved with FractionsCalc:
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4/27 + 2/9 = 10/27

Simplified Fraction

10/27

Mixed Number

Proper (10/27)

Decimal Value

0.37037

Percentage

37.037%

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Step-by-Step Solution: 4/27 + 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 4/27 by 1, and multiply the numerator and denominator of 2/9 by 3 so both fractions share the common base 27.

4 × 1/27 × 1 = 4/27 and 2 × 3/9 × 3 = 6/27

Step 3

Add the Numerators

Now add the numerators (4 + 6 = 10) and keep the common denominator 27 unchanged.

4 + 6/27 = 10/27

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 10 and 27 is 1, confirming that 10/27 cannot be reduced further—it is already in its simplest irreducible form.

10/27

Step 5

Decimal & Percentage Representation

Dividing the numerator 10 by denominator 27 produces a repeating decimal (approximately 0.37037, or 37.037%).

10 ÷ 27 = 0.37037 (37.037%)

Visual Representation

The diagram below illustrates 4/27 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`10/27`
Mixed Number Form	`10/27`
Decimal Form	`0.37037`
Percentage	`37.037%`

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Frequently Asked Questions

What is 4/27 plus 2/9 as a fraction?

4/27 + 2/9 in simplest fraction form is 10/27.

What is 4/27 plus 2/9 as a decimal?

4/27 + 2/9 converted to a decimal is 0.37037.

What is 4/27 plus 2/9 as a percentage?

4/27 + 2/9 expressed as a percentage is 37.037%.

Does 4/27 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.37037...) because the denominator contains prime factors other than 2 and 5.