What is 3/52 plus 2/9? (Answer: 131/468)

Exact Answer

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Problem: What is 3/52 plus 2/9?
Formula / Expression: 3/52 + 2/9
Final Answer: 131/468
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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 3/52 by 9, and multiply the numerator and denominator of 2/9 by 52 so both fractions share the common base 468.
Working: 3 × 9/52 × 9 = 27/468 and 2 × 52/9 × 52 = 104/468

Step 3: Add the Numerators
Now add the numerators (27 + 104 = 131) and keep the common denominator 468 unchanged.
Working: 27 + 104/468 = 131/468

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 131 and 468 is 1, confirming that 131/468 cannot be reduced further—it is already in its simplest irreducible form.
Working: 131/468

Step 5: Decimal & Percentage Representation
Dividing the numerator 131 by denominator 468 produces a repeating decimal (approximately 0.279915, or 27.9915%).
Working: 131 ÷ 468 = 0.279915 (27.9915%)

Key Values:
- Simplified Fraction: 131/468
- Mixed Number Form: 131/468
- Decimal Value: 0.279915
- Percentage: 27.9915%

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3/52 + 2/9 = 131/468

Simplified Fraction

131/468

Mixed Number

Proper (131/468)

Decimal Value

0.279915

Percentage

27.9915%

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Step-by-Step Solution: 3/52 + 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 3/52 by 9, and multiply the numerator and denominator of 2/9 by 52 so both fractions share the common base 468.

3 × 9/52 × 9 = 27/468 and 2 × 52/9 × 52 = 104/468

Step 3

Add the Numerators

Now add the numerators (27 + 104 = 131) and keep the common denominator 468 unchanged.

27 + 104/468 = 131/468

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 131 and 468 is 1, confirming that 131/468 cannot be reduced further—it is already in its simplest irreducible form.

131/468

Step 5

Decimal & Percentage Representation

Dividing the numerator 131 by denominator 468 produces a repeating decimal (approximately 0.279915, or 27.9915%).

131 ÷ 468 = 0.279915 (27.9915%)

Visual Representation

The diagram below illustrates 3/52 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`131/468`
Mixed Number Form	`131/468`
Decimal Form	`0.279915`
Percentage	`27.9915%`

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Frequently Asked Questions

What is 3/52 plus 2/9 as a fraction?

3/52 + 2/9 in simplest fraction form is 131/468.

What is 3/52 plus 2/9 as a decimal?

3/52 + 2/9 converted to a decimal is 0.279915.

What is 3/52 plus 2/9 as a percentage?

3/52 + 2/9 expressed as a percentage is 27.9915%.

Does 3/52 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.279915...) because the denominator contains prime factors other than 2 and 5.