What is 2/52 plus 2/9? (Answer: 61/234)

Exact Answer

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Problem: What is 2/52 plus 2/9?
Formula / Expression: 2/52 + 2/9
Final Answer: 61/234
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 52 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 52 × 9 = 468.
Working: LCD(52, 9) = 468

Step 2: Convert to Equivalent Fractions with Common Denominator 468
Multiply the numerator and denominator of 2/52 by 9, and multiply the numerator and denominator of 2/9 by 52 so both fractions share the common base 468.
Working: 2 × 9/52 × 9 = 18/468 and 2 × 52/9 × 52 = 104/468

Step 3: Add the Numerators
Now add the numerators (18 + 104 = 122) and keep the common denominator 468 unchanged.
Working: 18 + 104/468 = 122/468

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 122 and 468, which is 2. Divide both the numerator and denominator by 2.
Working: 122 ÷ 2/468 ÷ 2 = 61/234

Step 5: Decimal & Percentage Representation
Dividing the numerator 61 by denominator 234 produces a repeating decimal (approximately 0.260684, or 26.0684%).
Working: 61 ÷ 234 = 0.260684 (26.0684%)

Key Values:
- Simplified Fraction: 61/234
- Mixed Number Form: 61/234
- Decimal Value: 0.260684
- Percentage: 26.0684%

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Solved with FractionsCalc:
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2/52 + 2/9 = 61/234

Simplified Fraction

61/234

Mixed Number

Proper (61/234)

Decimal Value

0.260684

Percentage

26.0684%

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Step-by-Step Solution: 2/52 + 2/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 52 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 52 × 9 = 468.

LCD(52, 9) = 468

Step 2

Convert to Equivalent Fractions with Common Denominator 468

Multiply the numerator and denominator of 2/52 by 9, and multiply the numerator and denominator of 2/9 by 52 so both fractions share the common base 468.

2 × 9/52 × 9 = 18/468 and 2 × 52/9 × 52 = 104/468

Step 3

Add the Numerators

Now add the numerators (18 + 104 = 122) and keep the common denominator 468 unchanged.

18 + 104/468 = 122/468

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 122 and 468, which is 2. Divide both the numerator and denominator by 2.

122 ÷ 2/468 ÷ 2 = 61/234

Step 5

Decimal & Percentage Representation

Dividing the numerator 61 by denominator 234 produces a repeating decimal (approximately 0.260684, or 26.0684%).

61 ÷ 234 = 0.260684 (26.0684%)

Visual Representation

The diagram below illustrates 2/52 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`61/234`
Mixed Number Form	`61/234`
Decimal Form	`0.260684`
Percentage	`26.0684%`

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Frequently Asked Questions

What is 2/52 plus 2/9 as a fraction?

2/52 + 2/9 in simplest fraction form is 61/234.

What is 2/52 plus 2/9 as a decimal?

2/52 + 2/9 converted to a decimal is 0.260684.

What is 2/52 plus 2/9 as a percentage?

2/52 + 2/9 expressed as a percentage is 26.0684%.

Does 2/52 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.260684...) because the denominator contains prime factors other than 2 and 5.