What is 2/13 plus 3/7? (Answer: 53/91)

Exact Answer

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Problem: What is 2/13 plus 3/7?
Formula / Expression: 2/13 + 3/7
Final Answer: 53/91
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 13 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 7 = 91.
Working: LCD(13, 7) = 91

Step 2: Convert to Equivalent Fractions with Common Denominator 91
Multiply the numerator and denominator of 2/13 by 7, and multiply the numerator and denominator of 3/7 by 13 so both fractions share the common base 91.
Working: 2 × 7/13 × 7 = 14/91 and 3 × 13/7 × 13 = 39/91

Step 3: Add the Numerators
Now add the numerators (14 + 39 = 53) and keep the common denominator 91 unchanged.
Working: 14 + 39/91 = 53/91

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 53 and 91 is 1, confirming that 53/91 cannot be reduced further—it is already in its simplest irreducible form.
Working: 53/91

Step 5: Decimal & Percentage Representation
Dividing the numerator 53 by denominator 91 produces a repeating decimal (approximately 0.582418, or 58.2418%).
Working: 53 ÷ 91 = 0.582418 (58.2418%)

Key Values:
- Simplified Fraction: 53/91
- Mixed Number Form: 53/91
- Decimal Value: 0.582418
- Percentage: 58.2418%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-13-plus-3-7/
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2/13 + 3/7 = 53/91

Simplified Fraction

53/91

Mixed Number

Proper (53/91)

Decimal Value

0.582418

Percentage

58.2418%

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Step-by-Step Solution: 2/13 + 3/7

Step 1

Find the Least Common Denominator (LCD)

The denominators 13 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 7 = 91.

LCD(13, 7) = 91

Step 2

Convert to Equivalent Fractions with Common Denominator 91

Multiply the numerator and denominator of 2/13 by 7, and multiply the numerator and denominator of 3/7 by 13 so both fractions share the common base 91.

2 × 7/13 × 7 = 14/91 and 3 × 13/7 × 13 = 39/91

Step 3

Add the Numerators

Now add the numerators (14 + 39 = 53) and keep the common denominator 91 unchanged.

14 + 39/91 = 53/91

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 53 and 91 is 1, confirming that 53/91 cannot be reduced further—it is already in its simplest irreducible form.

53/91

Step 5

Decimal & Percentage Representation

Dividing the numerator 53 by denominator 91 produces a repeating decimal (approximately 0.582418, or 58.2418%).

53 ÷ 91 = 0.582418 (58.2418%)

Visual Representation

The diagram below illustrates 2/13 plus 3/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`53/91`
Mixed Number Form	`53/91`
Decimal Form	`0.582418`
Percentage	`58.2418%`

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Frequently Asked Questions

What is 2/13 plus 3/7 as a fraction?

2/13 + 3/7 in simplest fraction form is 53/91.

What is 2/13 plus 3/7 as a decimal?

2/13 + 3/7 converted to a decimal is 0.582418.

What is 2/13 plus 3/7 as a percentage?

2/13 + 3/7 expressed as a percentage is 58.2418%.

Does 2/13 plus 3/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.582418...) because the denominator contains prime factors other than 2 and 5.