What is 3/27 plus 2/9? (Answer: 1/3)

Exact Answer

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

Step 3: Add the Numerators
Now add the numerators (3 + 6 = 9) and keep the common denominator 27 unchanged.
Working: 3 + 6/27 = 9/27

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 9 and 27, which is 9. Divide both the numerator and denominator by 9.
Working: 9 ÷ 9/27 ÷ 9 = 1/3

Step 5: Decimal & Percentage Representation
Dividing the numerator 1 by denominator 3 produces a repeating decimal (approximately 0.333333, or 33.3333%).
Working: 1 ÷ 3 = 0.333333 (33.3333%)

Key Values:
- Simplified Fraction: 1/3
- Mixed Number Form: 1/3
- Decimal Value: 0.333333
- Percentage: 33.3333%

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Solved with FractionsCalc:
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3/27 + 2/9 = 1/3

Simplified Fraction

1/3

Mixed Number

Proper (1/3)

Decimal Value

0.333333

Percentage

33.3333%

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

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

Step 3

Add the Numerators

Now add the numerators (3 + 6 = 9) and keep the common denominator 27 unchanged.

3 + 6/27 = 9/27

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 9 and 27, which is 9. Divide both the numerator and denominator by 9.

9 ÷ 9/27 ÷ 9 = 1/3

Step 5

Decimal & Percentage Representation

Dividing the numerator 1 by denominator 3 produces a repeating decimal (approximately 0.333333, or 33.3333%).

1 ÷ 3 = 0.333333 (33.3333%)

Visual Representation

The diagram below illustrates 3/27 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`1/3`
Mixed Number Form	`1/3`
Decimal Form	`0.333333`
Percentage	`33.3333%`

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Frequently Asked Questions

What is 3/27 plus 2/9 as a fraction?

3/27 + 2/9 in simplest fraction form is 1/3.

What is 3/27 plus 2/9 as a decimal?

3/27 + 2/9 converted to a decimal is 0.333333.

What is 3/27 plus 2/9 as a percentage?

3/27 + 2/9 expressed as a percentage is 33.3333%.

Does 3/27 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.333333...) because the denominator contains prime factors other than 2 and 5.