What is 3/27 plus 2/3? (Answer: 7/9)

Exact Answer

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Problem: What is 3/27 plus 2/3?
Formula / Expression: 3/27 + 2/3
Final Answer: 7/9
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 27 is an exact multiple of 3 (3 × 9 = 27). The Least Common Denominator (LCD) is simply 27, meaning we only need to scale one fraction.
Working: LCD(27, 3) = 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 2/3 by 9 so both fractions share the common base 27.
Working: 3 × 1/27 × 1 = 3/27 and 2 × 9/3 × 9 = 18/27

Step 3: Add the Numerators
Now add the numerators (3 + 18 = 21) and keep the common denominator 27 unchanged.
Working: 3 + 18/27 = 21/27

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 21 and 27, which is 3. Divide both the numerator and denominator by 3.
Working: 21 ÷ 3/27 ÷ 3 = 7/9

Step 5: Decimal & Percentage Representation
Dividing the numerator 7 by denominator 9 produces a repeating decimal (approximately 0.777778, or 77.7778%).
Working: 7 ÷ 9 = 0.777778 (77.7778%)

Key Values:
- Simplified Fraction: 7/9
- Mixed Number Form: 7/9
- Decimal Value: 0.777778
- Percentage: 77.7778%

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Solved with FractionsCalc:
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3/27 + 2/3 = 7/9

Simplified Fraction

7/9

Mixed Number

Proper (7/9)

Decimal Value

0.777778

Percentage

77.7778%

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Step-by-Step Solution: 3/27 + 2/3

Step 1

Find the Least Common Denominator (LCD)

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

LCD(27, 3) = 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 2/3 by 9 so both fractions share the common base 27.

3 × 1/27 × 1 = 3/27 and 2 × 9/3 × 9 = 18/27

Step 3

Add the Numerators

Now add the numerators (3 + 18 = 21) and keep the common denominator 27 unchanged.

3 + 18/27 = 21/27

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 21 and 27, which is 3. Divide both the numerator and denominator by 3.

21 ÷ 3/27 ÷ 3 = 7/9

Step 5

Decimal & Percentage Representation

Dividing the numerator 7 by denominator 9 produces a repeating decimal (approximately 0.777778, or 77.7778%).

7 ÷ 9 = 0.777778 (77.7778%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`7/9`
Mixed Number Form	`7/9`
Decimal Form	`0.777778`
Percentage	`77.7778%`

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Frequently Asked Questions

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

3/27 + 2/3 in simplest fraction form is 7/9.

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

3/27 + 2/3 converted to a decimal is 0.777778.

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

3/27 + 2/3 expressed as a percentage is 77.7778%.

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

It results in a repeating decimal (approximately 0.777778...) because the denominator contains prime factors other than 2 and 5.