What is 2/53 plus 2/9? (Answer: 124/477)

Exact Answer

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Problem: What is 2/53 plus 2/9?
Formula / Expression: 2/53 + 2/9
Final Answer: 124/477
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 53 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 53 × 9 = 477.
Working: LCD(53, 9) = 477

Step 2: Convert to Equivalent Fractions with Common Denominator 477
Multiply the numerator and denominator of 2/53 by 9, and multiply the numerator and denominator of 2/9 by 53 so both fractions share the common base 477.
Working: 2 × 9/53 × 9 = 18/477 and 2 × 53/9 × 53 = 106/477

Step 3: Add the Numerators
Now add the numerators (18 + 106 = 124) and keep the common denominator 477 unchanged.
Working: 18 + 106/477 = 124/477

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 124 and 477 is 1, confirming that 124/477 cannot be reduced further—it is already in its simplest irreducible form.
Working: 124/477

Step 5: Decimal & Percentage Representation
Dividing the numerator 124 by denominator 477 produces a repeating decimal (approximately 0.259958, or 25.9958%).
Working: 124 ÷ 477 = 0.259958 (25.9958%)

Key Values:
- Simplified Fraction: 124/477
- Mixed Number Form: 124/477
- Decimal Value: 0.259958
- Percentage: 25.9958%

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Solved with FractionsCalc:
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2/53 + 2/9 = 124/477

Simplified Fraction

124/477

Mixed Number

Proper (124/477)

Decimal Value

0.259958

Percentage

25.9958%

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Step-by-Step Solution: 2/53 + 2/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 53 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 53 × 9 = 477.

LCD(53, 9) = 477

Step 2

Convert to Equivalent Fractions with Common Denominator 477

Multiply the numerator and denominator of 2/53 by 9, and multiply the numerator and denominator of 2/9 by 53 so both fractions share the common base 477.

2 × 9/53 × 9 = 18/477 and 2 × 53/9 × 53 = 106/477

Step 3

Add the Numerators

Now add the numerators (18 + 106 = 124) and keep the common denominator 477 unchanged.

18 + 106/477 = 124/477

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 124 and 477 is 1, confirming that 124/477 cannot be reduced further—it is already in its simplest irreducible form.

124/477

Step 5

Decimal & Percentage Representation

Dividing the numerator 124 by denominator 477 produces a repeating decimal (approximately 0.259958, or 25.9958%).

124 ÷ 477 = 0.259958 (25.9958%)

Visual Representation

The diagram below illustrates 2/53 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`124/477`
Mixed Number Form	`124/477`
Decimal Form	`0.259958`
Percentage	`25.9958%`

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Frequently Asked Questions

What is 2/53 plus 2/9 as a fraction?

2/53 + 2/9 in simplest fraction form is 124/477.

What is 2/53 plus 2/9 as a decimal?

2/53 + 2/9 converted to a decimal is 0.259958.

What is 2/53 plus 2/9 as a percentage?

2/53 + 2/9 expressed as a percentage is 25.9958%.

Does 2/53 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.259958...) because the denominator contains prime factors other than 2 and 5.