What is 2/13 plus 3/4? (Answer: 47/52)

Exact Answer

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Problem: What is 2/13 plus 3/4?
Formula / Expression: 2/13 + 3/4
Final Answer: 47/52
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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 2/13 by 4, and multiply the numerator and denominator of 3/4 by 13 so both fractions share the common base 52.
Working: 2 × 4/13 × 4 = 8/52 and 3 × 13/4 × 13 = 39/52

Step 3: Add the Numerators
Now add the numerators (8 + 39 = 47) and keep the common denominator 52 unchanged.
Working: 8 + 39/52 = 47/52

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 47 and 52 is 1, confirming that 47/52 cannot be reduced further—it is already in its simplest irreducible form.
Working: 47/52

Step 5: Decimal & Percentage Representation
Dividing the numerator 47 by denominator 52 produces a repeating decimal (approximately 0.903846, or 90.3846%).
Working: 47 ÷ 52 = 0.903846 (90.3846%)

Key Values:
- Simplified Fraction: 47/52
- Mixed Number Form: 47/52
- Decimal Value: 0.903846
- Percentage: 90.3846%

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Solved with FractionsCalc:
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2/13 + 3/4 = 47/52

Simplified Fraction

47/52

Mixed Number

Proper (47/52)

Decimal Value

0.903846

Percentage

90.3846%

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Step-by-Step Solution: 2/13 + 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 2/13 by 4, and multiply the numerator and denominator of 3/4 by 13 so both fractions share the common base 52.

2 × 4/13 × 4 = 8/52 and 3 × 13/4 × 13 = 39/52

Step 3

Add the Numerators

Now add the numerators (8 + 39 = 47) and keep the common denominator 52 unchanged.

8 + 39/52 = 47/52

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 47 and 52 is 1, confirming that 47/52 cannot be reduced further—it is already in its simplest irreducible form.

47/52

Step 5

Decimal & Percentage Representation

Dividing the numerator 47 by denominator 52 produces a repeating decimal (approximately 0.903846, or 90.3846%).

47 ÷ 52 = 0.903846 (90.3846%)

Visual Representation

The diagram below illustrates 2/13 plus 3/4 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`47/52`
Mixed Number Form	`47/52`
Decimal Form	`0.903846`
Percentage	`90.3846%`

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Frequently Asked Questions

What is 2/13 plus 3/4 as a fraction?

2/13 + 3/4 in simplest fraction form is 47/52.

What is 2/13 plus 3/4 as a decimal?

2/13 + 3/4 converted to a decimal is 0.903846.

What is 2/13 plus 3/4 as a percentage?

2/13 + 3/4 expressed as a percentage is 90.3846%.

Does 2/13 plus 3/4 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.903846...) because the denominator contains prime factors other than 2 and 5.