What is 5/48 plus 3/13? (Answer: 209/624)

Exact Answer

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Problem: What is 5/48 plus 3/13?
Formula / Expression: 5/48 + 3/13
Final Answer: 209/624
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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 5/48 by 13, and multiply the numerator and denominator of 3/13 by 48 so both fractions share the common base 624.
Working: 5 × 13/48 × 13 = 65/624 and 3 × 48/13 × 48 = 144/624

Step 3: Add the Numerators
Now add the numerators (65 + 144 = 209) and keep the common denominator 624 unchanged.
Working: 65 + 144/624 = 209/624

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 209 and 624 is 1, confirming that 209/624 cannot be reduced further—it is already in its simplest irreducible form.
Working: 209/624

Step 5: Decimal & Percentage Representation
Dividing the numerator 209 by denominator 624 produces a repeating decimal (approximately 0.334936, or 33.4936%).
Working: 209 ÷ 624 = 0.334936 (33.4936%)

Key Values:
- Simplified Fraction: 209/624
- Mixed Number Form: 209/624
- Decimal Value: 0.334936
- Percentage: 33.4936%

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Solved with FractionsCalc:
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5/48 + 3/13 = 209/624

Simplified Fraction

209/624

Mixed Number

Proper (209/624)

Decimal Value

0.334936

Percentage

33.4936%

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Step-by-Step Solution: 5/48 + 3/13

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 5/48 by 13, and multiply the numerator and denominator of 3/13 by 48 so both fractions share the common base 624.

5 × 13/48 × 13 = 65/624 and 3 × 48/13 × 48 = 144/624

Step 3

Add the Numerators

Now add the numerators (65 + 144 = 209) and keep the common denominator 624 unchanged.

65 + 144/624 = 209/624

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 209 and 624 is 1, confirming that 209/624 cannot be reduced further—it is already in its simplest irreducible form.

209/624

Step 5

Decimal & Percentage Representation

Dividing the numerator 209 by denominator 624 produces a repeating decimal (approximately 0.334936, or 33.4936%).

209 ÷ 624 = 0.334936 (33.4936%)

Visual Representation

The diagram below illustrates 5/48 plus 3/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`209/624`
Mixed Number Form	`209/624`
Decimal Form	`0.334936`
Percentage	`33.4936%`

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Frequently Asked Questions

What is 5/48 plus 3/13 as a fraction?

5/48 + 3/13 in simplest fraction form is 209/624.

What is 5/48 plus 3/13 as a decimal?

5/48 + 3/13 converted to a decimal is 0.334936.

What is 5/48 plus 3/13 as a percentage?

5/48 + 3/13 expressed as a percentage is 33.4936%.

Does 5/48 plus 3/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.334936...) because the denominator contains prime factors other than 2 and 5.