What is 2/7 plus 9/13? (Answer: 89/91)

Exact Answer

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Problem: What is 2/7 plus 9/13?
Formula / Expression: 2/7 + 9/13
Final Answer: 89/91
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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 9/13 by 7 so both fractions share the common base 91.
Working: 2 × 13/7 × 13 = 26/91 and 9 × 7/13 × 7 = 63/91

Step 3: Add the Numerators
Now add the numerators (26 + 63 = 89) and keep the common denominator 91 unchanged.
Working: 26 + 63/91 = 89/91

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 89 and 91 is 1, confirming that 89/91 cannot be reduced further—it is already in its simplest irreducible form.
Working: 89/91

Step 5: Decimal & Percentage Representation
Dividing the numerator 89 by denominator 91 produces a repeating decimal (approximately 0.978022, or 97.8022%).
Working: 89 ÷ 91 = 0.978022 (97.8022%)

Key Values:
- Simplified Fraction: 89/91
- Mixed Number Form: 89/91
- Decimal Value: 0.978022
- Percentage: 97.8022%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-7-plus-9-13/
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2/7 + 9/13 = 89/91

Simplified Fraction

89/91

Mixed Number

Proper (89/91)

Decimal Value

0.978022

Percentage

97.8022%

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Step-by-Step Solution: 2/7 + 9/13

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 9/13 by 7 so both fractions share the common base 91.

2 × 13/7 × 13 = 26/91 and 9 × 7/13 × 7 = 63/91

Step 3

Add the Numerators

Now add the numerators (26 + 63 = 89) and keep the common denominator 91 unchanged.

26 + 63/91 = 89/91

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 89 and 91 is 1, confirming that 89/91 cannot be reduced further—it is already in its simplest irreducible form.

89/91

Step 5

Decimal & Percentage Representation

Dividing the numerator 89 by denominator 91 produces a repeating decimal (approximately 0.978022, or 97.8022%).

89 ÷ 91 = 0.978022 (97.8022%)

Visual Representation

The diagram below illustrates 2/7 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`89/91`
Mixed Number Form	`89/91`
Decimal Form	`0.978022`
Percentage	`97.8022%`

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Frequently Asked Questions

What is 2/7 plus 9/13 as a fraction?

2/7 + 9/13 in simplest fraction form is 89/91.

What is 2/7 plus 9/13 as a decimal?

2/7 + 9/13 converted to a decimal is 0.978022.

What is 2/7 plus 9/13 as a percentage?

2/7 + 9/13 expressed as a percentage is 97.8022%.

Does 2/7 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.978022...) because the denominator contains prime factors other than 2 and 5.