What is 3/55 plus 3/13? (Answer: 204/715)

Exact Answer

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Problem: What is 3/55 plus 3/13?
Formula / Expression: 3/55 + 3/13
Final Answer: 204/715
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 55 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 55 × 13 = 715.
Working: LCD(55, 13) = 715

Step 2: Convert to Equivalent Fractions with Common Denominator 715
Multiply the numerator and denominator of 3/55 by 13, and multiply the numerator and denominator of 3/13 by 55 so both fractions share the common base 715.
Working: 3 × 13/55 × 13 = 39/715 and 3 × 55/13 × 55 = 165/715

Step 3: Add the Numerators
Now add the numerators (39 + 165 = 204) and keep the common denominator 715 unchanged.
Working: 39 + 165/715 = 204/715

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 204 and 715 is 1, confirming that 204/715 cannot be reduced further—it is already in its simplest irreducible form.
Working: 204/715

Step 5: Decimal & Percentage Representation
Dividing the numerator 204 by denominator 715 produces a repeating decimal (approximately 0.285315, or 28.5315%).
Working: 204 ÷ 715 = 0.285315 (28.5315%)

Key Values:
- Simplified Fraction: 204/715
- Mixed Number Form: 204/715
- Decimal Value: 0.285315
- Percentage: 28.5315%

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3/55 + 3/13 = 204/715

Simplified Fraction

204/715

Mixed Number

Proper (204/715)

Decimal Value

0.285315

Percentage

28.5315%

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Step-by-Step Solution: 3/55 + 3/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 55 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 55 × 13 = 715.

LCD(55, 13) = 715

Step 2

Convert to Equivalent Fractions with Common Denominator 715

Multiply the numerator and denominator of 3/55 by 13, and multiply the numerator and denominator of 3/13 by 55 so both fractions share the common base 715.

3 × 13/55 × 13 = 39/715 and 3 × 55/13 × 55 = 165/715

Step 3

Add the Numerators

Now add the numerators (39 + 165 = 204) and keep the common denominator 715 unchanged.

39 + 165/715 = 204/715

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 204 and 715 is 1, confirming that 204/715 cannot be reduced further—it is already in its simplest irreducible form.

204/715

Step 5

Decimal & Percentage Representation

Dividing the numerator 204 by denominator 715 produces a repeating decimal (approximately 0.285315, or 28.5315%).

204 ÷ 715 = 0.285315 (28.5315%)

Visual Representation

The diagram below illustrates 3/55 plus 3/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`204/715`
Mixed Number Form	`204/715`
Decimal Form	`0.285315`
Percentage	`28.5315%`

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Frequently Asked Questions

What is 3/55 plus 3/13 as a fraction?

3/55 + 3/13 in simplest fraction form is 204/715.

What is 3/55 plus 3/13 as a decimal?

3/55 + 3/13 converted to a decimal is 0.285315.

What is 3/55 plus 3/13 as a percentage?

3/55 + 3/13 expressed as a percentage is 28.5315%.

Does 3/55 plus 3/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.285315...) because the denominator contains prime factors other than 2 and 5.