What is 1/7 plus 8/13? (Answer: 69/91)

Exact Answer

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Problem: What is 1/7 plus 8/13?
Formula / Expression: 1/7 + 8/13
Final Answer: 69/91
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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 8/13 by 7 so both fractions share the common base 91.
Working: 1 × 13/7 × 13 = 13/91 and 8 × 7/13 × 7 = 56/91

Step 3: Add the Numerators
Now add the numerators (13 + 56 = 69) and keep the common denominator 91 unchanged.
Working: 13 + 56/91 = 69/91

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 69 and 91 is 1, confirming that 69/91 cannot be reduced further—it is already in its simplest irreducible form.
Working: 69/91

Step 5: Decimal & Percentage Representation
Dividing the numerator 69 by denominator 91 produces a repeating decimal (approximately 0.758242, or 75.8242%).
Working: 69 ÷ 91 = 0.758242 (75.8242%)

Key Values:
- Simplified Fraction: 69/91
- Mixed Number Form: 69/91
- Decimal Value: 0.758242
- Percentage: 75.8242%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-7-plus-8-13/
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1/7 + 8/13 = 69/91

Simplified Fraction

69/91

Mixed Number

Proper (69/91)

Decimal Value

0.758242

Percentage

75.8242%

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Step-by-Step Solution: 1/7 + 8/13

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 8/13 by 7 so both fractions share the common base 91.

1 × 13/7 × 13 = 13/91 and 8 × 7/13 × 7 = 56/91

Step 3

Add the Numerators

Now add the numerators (13 + 56 = 69) and keep the common denominator 91 unchanged.

13 + 56/91 = 69/91

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 69 and 91 is 1, confirming that 69/91 cannot be reduced further—it is already in its simplest irreducible form.

69/91

Step 5

Decimal & Percentage Representation

Dividing the numerator 69 by denominator 91 produces a repeating decimal (approximately 0.758242, or 75.8242%).

69 ÷ 91 = 0.758242 (75.8242%)

Visual Representation

The diagram below illustrates 1/7 plus 8/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`69/91`
Mixed Number Form	`69/91`
Decimal Form	`0.758242`
Percentage	`75.8242%`

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Frequently Asked Questions

What is 1/7 plus 8/13 as a fraction?

1/7 + 8/13 in simplest fraction form is 69/91.

What is 1/7 plus 8/13 as a decimal?

1/7 + 8/13 converted to a decimal is 0.758242.

What is 1/7 plus 8/13 as a percentage?

1/7 + 8/13 expressed as a percentage is 75.8242%.

Does 1/7 plus 8/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.758242...) because the denominator contains prime factors other than 2 and 5.