What is 13/48 plus 5/13? (Answer: 409/624)

Exact Answer

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Problem: What is 13/48 plus 5/13?
Formula / Expression: 13/48 + 5/13
Final Answer: 409/624
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 48 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 48 × 13 = 624.
Working: LCD(48, 13) = 624

Step 2: Convert to Equivalent Fractions with Common Denominator 624
Multiply the numerator and denominator of 13/48 by 13, and multiply the numerator and denominator of 5/13 by 48 so both fractions share the common base 624.
Working: 13 × 13/48 × 13 = 169/624 and 5 × 48/13 × 48 = 240/624

Step 3: Add the Numerators
Now add the numerators (169 + 240 = 409) and keep the common denominator 624 unchanged.
Working: 169 + 240/624 = 409/624

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 409 and 624 is 1, confirming that 409/624 cannot be reduced further—it is already in its simplest irreducible form.
Working: 409/624

Step 5: Decimal & Percentage Representation
Dividing the numerator 409 by denominator 624 produces a repeating decimal (approximately 0.655449, or 65.5449%).
Working: 409 ÷ 624 = 0.655449 (65.5449%)

Key Values:
- Simplified Fraction: 409/624
- Mixed Number Form: 409/624
- Decimal Value: 0.655449
- Percentage: 65.5449%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-13-48-plus-5-13/
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13/48 + 5/13 = 409/624

Simplified Fraction

409/624

Mixed Number

Proper (409/624)

Decimal Value

0.655449

Percentage

65.5449%

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Step-by-Step Solution: 13/48 + 5/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 48 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 48 × 13 = 624.

LCD(48, 13) = 624

Step 2

Convert to Equivalent Fractions with Common Denominator 624

Multiply the numerator and denominator of 13/48 by 13, and multiply the numerator and denominator of 5/13 by 48 so both fractions share the common base 624.

13 × 13/48 × 13 = 169/624 and 5 × 48/13 × 48 = 240/624

Step 3

Add the Numerators

Now add the numerators (169 + 240 = 409) and keep the common denominator 624 unchanged.

169 + 240/624 = 409/624

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 409 and 624 is 1, confirming that 409/624 cannot be reduced further—it is already in its simplest irreducible form.

409/624

Step 5

Decimal & Percentage Representation

Dividing the numerator 409 by denominator 624 produces a repeating decimal (approximately 0.655449, or 65.5449%).

409 ÷ 624 = 0.655449 (65.5449%)

Visual Representation

The diagram below illustrates 13/48 plus 5/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`409/624`
Mixed Number Form	`409/624`
Decimal Form	`0.655449`
Percentage	`65.5449%`

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Frequently Asked Questions

What is 13/48 plus 5/13 as a fraction?

13/48 + 5/13 in simplest fraction form is 409/624.

What is 13/48 plus 5/13 as a decimal?

13/48 + 5/13 converted to a decimal is 0.655449.

What is 13/48 plus 5/13 as a percentage?

13/48 + 5/13 expressed as a percentage is 65.5449%.

Does 13/48 plus 5/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.655449...) because the denominator contains prime factors other than 2 and 5.