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

Exact Answer

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Problem: What is 3/9 plus 9/27?
Formula / Expression: 3/9 + 9/27
Final Answer: 2/3
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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(9, 27) = 27

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

Step 3: Add the Numerators
Now add the numerators (9 + 9 = 18) and keep the common denominator 27 unchanged.
Working: 9 + 9/27 = 18/27

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 18 and 27, which is 9. Divide both the numerator and denominator by 9.
Working: 18 ÷ 9/27 ÷ 9 = 2/3

Step 5: Decimal & Percentage Representation
Dividing the numerator 2 by denominator 3 produces a repeating decimal (approximately 0.666667, or 66.6667%).
Working: 2 ÷ 3 = 0.666667 (66.6667%)

Key Values:
- Simplified Fraction: 2/3
- Mixed Number Form: 2/3
- Decimal Value: 0.666667
- Percentage: 66.6667%

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

Simplified Fraction

2/3

Mixed Number

Proper (2/3)

Decimal Value

0.666667

Percentage

66.6667%

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Step-by-Step Solution: 3/9 + 9/27

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

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

Step 3

Add the Numerators

Now add the numerators (9 + 9 = 18) and keep the common denominator 27 unchanged.

9 + 9/27 = 18/27

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 18 and 27, which is 9. Divide both the numerator and denominator by 9.

18 ÷ 9/27 ÷ 9 = 2/3

Step 5

Decimal & Percentage Representation

Dividing the numerator 2 by denominator 3 produces a repeating decimal (approximately 0.666667, or 66.6667%).

2 ÷ 3 = 0.666667 (66.6667%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`2/3`
Mixed Number Form	`2/3`
Decimal Form	`0.666667`
Percentage	`66.6667%`

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Frequently Asked Questions

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

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

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

3/9 + 9/27 converted to a decimal is 0.666667.

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

3/9 + 9/27 expressed as a percentage is 66.6667%.

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

It results in a repeating decimal (approximately 0.666667...) because the denominator contains prime factors other than 2 and 5.