What is 2/54 plus 2/9? (Answer: 7/27)

Exact Answer

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Problem: What is 2/54 plus 2/9?
Formula / Expression: 2/54 + 2/9
Final Answer: 7/27
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 54 is an exact multiple of 9 (9 × 6 = 54). The Least Common Denominator (LCD) is simply 54, meaning we only need to scale one fraction.
Working: LCD(54, 9) = 54

Step 2: Convert to Equivalent Fractions with Common Denominator 54
Multiply the numerator and denominator of 2/54 by 1, and multiply the numerator and denominator of 2/9 by 6 so both fractions share the common base 54.
Working: 2 × 1/54 × 1 = 2/54 and 2 × 6/9 × 6 = 12/54

Step 3: Add the Numerators
Now add the numerators (2 + 12 = 14) and keep the common denominator 54 unchanged.
Working: 2 + 12/54 = 14/54

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 14 and 54, which is 2. Divide both the numerator and denominator by 2.
Working: 14 ÷ 2/54 ÷ 2 = 7/27

Step 5: Decimal & Percentage Representation
Dividing the numerator 7 by denominator 27 produces a repeating decimal (approximately 0.259259, or 25.9259%).
Working: 7 ÷ 27 = 0.259259 (25.9259%)

Key Values:
- Simplified Fraction: 7/27
- Mixed Number Form: 7/27
- Decimal Value: 0.259259
- Percentage: 25.9259%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-54-plus-2-9/
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2/54 + 2/9 = 7/27

Simplified Fraction

7/27

Mixed Number

Proper (7/27)

Decimal Value

0.259259

Percentage

25.9259%

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Step-by-Step Solution: 2/54 + 2/9

Step 1

Find the Least Common Denominator (LCD)

Notice that 54 is an exact multiple of 9 (9 × 6 = 54). The Least Common Denominator (LCD) is simply 54, meaning we only need to scale one fraction.

LCD(54, 9) = 54

Step 2

Convert to Equivalent Fractions with Common Denominator 54

Multiply the numerator and denominator of 2/54 by 1, and multiply the numerator and denominator of 2/9 by 6 so both fractions share the common base 54.

2 × 1/54 × 1 = 2/54 and 2 × 6/9 × 6 = 12/54

Step 3

Add the Numerators

Now add the numerators (2 + 12 = 14) and keep the common denominator 54 unchanged.

2 + 12/54 = 14/54

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 14 and 54, which is 2. Divide both the numerator and denominator by 2.

14 ÷ 2/54 ÷ 2 = 7/27

Step 5

Decimal & Percentage Representation

Dividing the numerator 7 by denominator 27 produces a repeating decimal (approximately 0.259259, or 25.9259%).

7 ÷ 27 = 0.259259 (25.9259%)

Visual Representation

The diagram below illustrates 2/54 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`7/27`
Mixed Number Form	`7/27`
Decimal Form	`0.259259`
Percentage	`25.9259%`

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Frequently Asked Questions

What is 2/54 plus 2/9 as a fraction?

2/54 + 2/9 in simplest fraction form is 7/27.

What is 2/54 plus 2/9 as a decimal?

2/54 + 2/9 converted to a decimal is 0.259259.

What is 2/54 plus 2/9 as a percentage?

2/54 + 2/9 expressed as a percentage is 25.9259%.

Does 2/54 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.259259...) because the denominator contains prime factors other than 2 and 5.