What is 2/7 plus 5/13? (Answer: 61/91)

Exact Answer

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Problem: What is 2/7 plus 5/13?
Formula / Expression: 2/7 + 5/13
Final Answer: 61/91
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 91
Multiply the numerator and denominator of 2/7 by 13, and multiply the numerator and denominator of 5/13 by 7 so both fractions share the common base 91.
Working: 2 × 13/7 × 13 = 26/91 and 5 × 7/13 × 7 = 35/91

Step 3: Add the Numerators
Now add the numerators (26 + 35 = 61) and keep the common denominator 91 unchanged.
Working: 26 + 35/91 = 61/91

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 61 and 91 is 1, confirming that 61/91 cannot be reduced further—it is already in its simplest irreducible form.
Working: 61/91

Step 5: Decimal & Percentage Representation
Dividing the numerator 61 by denominator 91 produces a repeating decimal (approximately 0.67033, or 67.033%).
Working: 61 ÷ 91 = 0.67033 (67.033%)

Key Values:
- Simplified Fraction: 61/91
- Mixed Number Form: 61/91
- Decimal Value: 0.67033
- Percentage: 67.033%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-7-plus-5-13/
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2/7 + 5/13 = 61/91

Simplified Fraction

61/91

Mixed Number

Proper (61/91)

Decimal Value

0.67033

Percentage

67.033%

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Step-by-Step Solution: 2/7 + 5/13

Step 1

Find the Least Common Denominator (LCD)

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

LCD(7, 13) = 91

Step 2

Convert to Equivalent Fractions with Common Denominator 91

Multiply the numerator and denominator of 2/7 by 13, and multiply the numerator and denominator of 5/13 by 7 so both fractions share the common base 91.

2 × 13/7 × 13 = 26/91 and 5 × 7/13 × 7 = 35/91

Step 3

Add the Numerators

Now add the numerators (26 + 35 = 61) and keep the common denominator 91 unchanged.

26 + 35/91 = 61/91

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 61 and 91 is 1, confirming that 61/91 cannot be reduced further—it is already in its simplest irreducible form.

61/91

Step 5

Decimal & Percentage Representation

Dividing the numerator 61 by denominator 91 produces a repeating decimal (approximately 0.67033, or 67.033%).

61 ÷ 91 = 0.67033 (67.033%)

Visual Representation

The diagram below illustrates 2/7 plus 5/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`61/91`
Mixed Number Form	`61/91`
Decimal Form	`0.67033`
Percentage	`67.033%`

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Frequently Asked Questions

What is 2/7 plus 5/13 as a fraction?

2/7 + 5/13 in simplest fraction form is 61/91.

What is 2/7 plus 5/13 as a decimal?

2/7 + 5/13 converted to a decimal is 0.67033.

What is 2/7 plus 5/13 as a percentage?

2/7 + 5/13 expressed as a percentage is 67.033%.

Does 2/7 plus 5/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.67033...) because the denominator contains prime factors other than 2 and 5.