What is 3/13 plus 3/4? (Answer: 51/52)

Exact Answer

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Problem: What is 3/13 plus 3/4?
Formula / Expression: 3/13 + 3/4
Final Answer: 51/52
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 13 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 4 = 52.
Working: LCD(13, 4) = 52

Step 2: Convert to Equivalent Fractions with Common Denominator 52
Multiply the numerator and denominator of 3/13 by 4, and multiply the numerator and denominator of 3/4 by 13 so both fractions share the common base 52.
Working: 3 × 4/13 × 4 = 12/52 and 3 × 13/4 × 13 = 39/52

Step 3: Add the Numerators
Now add the numerators (12 + 39 = 51) and keep the common denominator 52 unchanged.
Working: 12 + 39/52 = 51/52

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 51 and 52 is 1, confirming that 51/52 cannot be reduced further—it is already in its simplest irreducible form.
Working: 51/52

Step 5: Decimal & Percentage Representation
Dividing the numerator 51 by denominator 52 produces a repeating decimal (approximately 0.980769, or 98.0769%).
Working: 51 ÷ 52 = 0.980769 (98.0769%)

Key Values:
- Simplified Fraction: 51/52
- Mixed Number Form: 51/52
- Decimal Value: 0.980769
- Percentage: 98.0769%

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Solved with FractionsCalc:
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3/13 + 3/4 = 51/52

Simplified Fraction

51/52

Mixed Number

Proper (51/52)

Decimal Value

0.980769

Percentage

98.0769%

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Step-by-Step Solution: 3/13 + 3/4

Step 1

Find the Least Common Denominator (LCD)

The denominators 13 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 4 = 52.

LCD(13, 4) = 52

Step 2

Convert to Equivalent Fractions with Common Denominator 52

Multiply the numerator and denominator of 3/13 by 4, and multiply the numerator and denominator of 3/4 by 13 so both fractions share the common base 52.

3 × 4/13 × 4 = 12/52 and 3 × 13/4 × 13 = 39/52

Step 3

Add the Numerators

Now add the numerators (12 + 39 = 51) and keep the common denominator 52 unchanged.

12 + 39/52 = 51/52

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 51 and 52 is 1, confirming that 51/52 cannot be reduced further—it is already in its simplest irreducible form.

51/52

Step 5

Decimal & Percentage Representation

Dividing the numerator 51 by denominator 52 produces a repeating decimal (approximately 0.980769, or 98.0769%).

51 ÷ 52 = 0.980769 (98.0769%)

Visual Representation

The diagram below illustrates 3/13 plus 3/4 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`51/52`
Mixed Number Form	`51/52`
Decimal Form	`0.980769`
Percentage	`98.0769%`

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Frequently Asked Questions

What is 3/13 plus 3/4 as a fraction?

3/13 + 3/4 in simplest fraction form is 51/52.

What is 3/13 plus 3/4 as a decimal?

3/13 + 3/4 converted to a decimal is 0.980769.

What is 3/13 plus 3/4 as a percentage?

3/13 + 3/4 expressed as a percentage is 98.0769%.

Does 3/13 plus 3/4 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.980769...) because the denominator contains prime factors other than 2 and 5.