What is 1/7 plus 9/13? (Answer: 76/91)

Exact Answer

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Problem: What is 1/7 plus 9/13?
Formula / Expression: 1/7 + 9/13
Final Answer: 76/91
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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 1/7 by 13, and multiply the numerator and denominator of 9/13 by 7 so both fractions share the common base 91.
Working: 1 × 13/7 × 13 = 13/91 and 9 × 7/13 × 7 = 63/91

Step 3: Add the Numerators
Now add the numerators (13 + 63 = 76) and keep the common denominator 91 unchanged.
Working: 13 + 63/91 = 76/91

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 76 and 91 is 1, confirming that 76/91 cannot be reduced further—it is already in its simplest irreducible form.
Working: 76/91

Step 5: Decimal & Percentage Representation
Dividing the numerator 76 by denominator 91 produces a repeating decimal (approximately 0.835165, or 83.5165%).
Working: 76 ÷ 91 = 0.835165 (83.5165%)

Key Values:
- Simplified Fraction: 76/91
- Mixed Number Form: 76/91
- Decimal Value: 0.835165
- Percentage: 83.5165%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-7-plus-9-13/
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1/7 + 9/13 = 76/91

Simplified Fraction

76/91

Mixed Number

Proper (76/91)

Decimal Value

0.835165

Percentage

83.5165%

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Step-by-Step Solution: 1/7 + 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 1/7 by 13, and multiply the numerator and denominator of 9/13 by 7 so both fractions share the common base 91.

1 × 13/7 × 13 = 13/91 and 9 × 7/13 × 7 = 63/91

Step 3

Add the Numerators

Now add the numerators (13 + 63 = 76) and keep the common denominator 91 unchanged.

13 + 63/91 = 76/91

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 76 and 91 is 1, confirming that 76/91 cannot be reduced further—it is already in its simplest irreducible form.

76/91

Step 5

Decimal & Percentage Representation

Dividing the numerator 76 by denominator 91 produces a repeating decimal (approximately 0.835165, or 83.5165%).

76 ÷ 91 = 0.835165 (83.5165%)

Visual Representation

The diagram below illustrates 1/7 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`76/91`
Mixed Number Form	`76/91`
Decimal Form	`0.835165`
Percentage	`83.5165%`

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Frequently Asked Questions

What is 1/7 plus 9/13 as a fraction?

1/7 + 9/13 in simplest fraction form is 76/91.

What is 1/7 plus 9/13 as a decimal?

1/7 + 9/13 converted to a decimal is 0.835165.

What is 1/7 plus 9/13 as a percentage?

1/7 + 9/13 expressed as a percentage is 83.5165%.

Does 1/7 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.835165...) because the denominator contains prime factors other than 2 and 5.