What is 5/51 plus 3/13? (Answer: 218/663)

Exact Answer

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Problem: What is 5/51 plus 3/13?
Formula / Expression: 5/51 + 3/13
Final Answer: 218/663
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 51 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 51 × 13 = 663.
Working: LCD(51, 13) = 663

Step 2: Convert to Equivalent Fractions with Common Denominator 663
Multiply the numerator and denominator of 5/51 by 13, and multiply the numerator and denominator of 3/13 by 51 so both fractions share the common base 663.
Working: 5 × 13/51 × 13 = 65/663 and 3 × 51/13 × 51 = 153/663

Step 3: Add the Numerators
Now add the numerators (65 + 153 = 218) and keep the common denominator 663 unchanged.
Working: 65 + 153/663 = 218/663

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 218 and 663 is 1, confirming that 218/663 cannot be reduced further—it is already in its simplest irreducible form.
Working: 218/663

Step 5: Decimal & Percentage Representation
Dividing the numerator 218 by denominator 663 produces a repeating decimal (approximately 0.328808, or 32.8808%).
Working: 218 ÷ 663 = 0.328808 (32.8808%)

Key Values:
- Simplified Fraction: 218/663
- Mixed Number Form: 218/663
- Decimal Value: 0.328808
- Percentage: 32.8808%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-51-plus-3-13/
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5/51 + 3/13 = 218/663

Simplified Fraction

218/663

Mixed Number

Proper (218/663)

Decimal Value

0.328808

Percentage

32.8808%

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Step-by-Step Solution: 5/51 + 3/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 51 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 51 × 13 = 663.

LCD(51, 13) = 663

Step 2

Convert to Equivalent Fractions with Common Denominator 663

Multiply the numerator and denominator of 5/51 by 13, and multiply the numerator and denominator of 3/13 by 51 so both fractions share the common base 663.

5 × 13/51 × 13 = 65/663 and 3 × 51/13 × 51 = 153/663

Step 3

Add the Numerators

Now add the numerators (65 + 153 = 218) and keep the common denominator 663 unchanged.

65 + 153/663 = 218/663

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 218 and 663 is 1, confirming that 218/663 cannot be reduced further—it is already in its simplest irreducible form.

218/663

Step 5

Decimal & Percentage Representation

Dividing the numerator 218 by denominator 663 produces a repeating decimal (approximately 0.328808, or 32.8808%).

218 ÷ 663 = 0.328808 (32.8808%)

Visual Representation

The diagram below illustrates 5/51 plus 3/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`218/663`
Mixed Number Form	`218/663`
Decimal Form	`0.328808`
Percentage	`32.8808%`

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Frequently Asked Questions

What is 5/51 plus 3/13 as a fraction?

5/51 + 3/13 in simplest fraction form is 218/663.

What is 5/51 plus 3/13 as a decimal?

5/51 + 3/13 converted to a decimal is 0.328808.

What is 5/51 plus 3/13 as a percentage?

5/51 + 3/13 expressed as a percentage is 32.8808%.

Does 5/51 plus 3/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.328808...) because the denominator contains prime factors other than 2 and 5.