What is 2/13 plus 5/7? (Answer: 79/91)

Exact Answer

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Problem: What is 2/13 plus 5/7?
Formula / Expression: 2/13 + 5/7
Final Answer: 79/91
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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 5/7 by 13 so both fractions share the common base 91.
Working: 2 × 7/13 × 7 = 14/91 and 5 × 13/7 × 13 = 65/91

Step 3: Add the Numerators
Now add the numerators (14 + 65 = 79) and keep the common denominator 91 unchanged.
Working: 14 + 65/91 = 79/91

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 79 and 91 is 1, confirming that 79/91 cannot be reduced further—it is already in its simplest irreducible form.
Working: 79/91

Step 5: Decimal & Percentage Representation
Dividing the numerator 79 by denominator 91 produces a repeating decimal (approximately 0.868132, or 86.8132%).
Working: 79 ÷ 91 = 0.868132 (86.8132%)

Key Values:
- Simplified Fraction: 79/91
- Mixed Number Form: 79/91
- Decimal Value: 0.868132
- Percentage: 86.8132%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-13-plus-5-7/
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2/13 + 5/7 = 79/91

Simplified Fraction

79/91

Mixed Number

Proper (79/91)

Decimal Value

0.868132

Percentage

86.8132%

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

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 5/7 by 13 so both fractions share the common base 91.

2 × 7/13 × 7 = 14/91 and 5 × 13/7 × 13 = 65/91

Step 3

Add the Numerators

Now add the numerators (14 + 65 = 79) and keep the common denominator 91 unchanged.

14 + 65/91 = 79/91

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 79 and 91 is 1, confirming that 79/91 cannot be reduced further—it is already in its simplest irreducible form.

79/91

Step 5

Decimal & Percentage Representation

Dividing the numerator 79 by denominator 91 produces a repeating decimal (approximately 0.868132, or 86.8132%).

79 ÷ 91 = 0.868132 (86.8132%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`79/91`
Mixed Number Form	`79/91`
Decimal Form	`0.868132`
Percentage	`86.8132%`

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Frequently Asked Questions

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

2/13 + 5/7 in simplest fraction form is 79/91.

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

2/13 + 5/7 converted to a decimal is 0.868132.

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

2/13 + 5/7 expressed as a percentage is 86.8132%.

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

It results in a repeating decimal (approximately 0.868132...) because the denominator contains prime factors other than 2 and 5.