What is 3/7 plus 11/13? (Answer: 116/91)

Exact Answer

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Problem: What is 3/7 plus 11/13?
Formula / Expression: 3/7 + 11/13
Final Answer: 1 25/91 (116/91)
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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 3/7 by 13, and multiply the numerator and denominator of 11/13 by 7 so both fractions share the common base 91.
Working: 3 × 13/7 × 13 = 39/91 and 11 × 7/13 × 7 = 77/91

Step 3: Add the Numerators
Now add the numerators (39 + 77 = 116) and keep the common denominator 91 unchanged.
Working: 39 + 77/91 = 116/91

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 116 and 91 is 1, confirming that 116/91 cannot be reduced further—it is already in its simplest irreducible form.
Working: 116/91

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (116) is greater than the denominator (91), divide 116 by 91: it goes in 1 whole time(s) with a remainder of 25, giving the mixed number 1 25/91.
Working: 116/91 = 1 25/91

Step 6: Decimal & Percentage Representation
Dividing the numerator 116 by denominator 91 produces a repeating decimal (approximately 1.274725, or 127.4725%).
Working: 116 ÷ 91 = 1.274725 (127.4725%)

Key Values:
- Simplified Fraction: 116/91
- Mixed Number Form: 1 25/91
- Decimal Value: 1.274725
- Percentage: 127.4725%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-7-plus-11-13/
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3/7 + 11/13 = 116/91

Simplified Fraction

116/91

Mixed Number

1 25/91

Decimal Value

1.274725

Percentage

127.4725%

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Step-by-Step Solution: 3/7 + 11/13

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 3/7 by 13, and multiply the numerator and denominator of 11/13 by 7 so both fractions share the common base 91.

3 × 13/7 × 13 = 39/91 and 11 × 7/13 × 7 = 77/91

Step 3

Add the Numerators

Now add the numerators (39 + 77 = 116) and keep the common denominator 91 unchanged.

39 + 77/91 = 116/91

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 116 and 91 is 1, confirming that 116/91 cannot be reduced further—it is already in its simplest irreducible form.

116/91

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (116) is greater than the denominator (91), divide 116 by 91: it goes in 1 whole time(s) with a remainder of 25, giving the mixed number 1 25/91.

116/91 = 125/91

Step 6

Decimal & Percentage Representation

Dividing the numerator 116 by denominator 91 produces a repeating decimal (approximately 1.274725, or 127.4725%).

116 ÷ 91 = 1.274725 (127.4725%)

Visual Representation

The diagram below illustrates 3/7 plus 11/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`116/91`
Mixed Number Form	`1 25/91`
Decimal Form	`1.274725`
Percentage	`127.4725%`

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Frequently Asked Questions

What is 3/7 plus 11/13 as a fraction?

3/7 + 11/13 in simplest fraction form is 116/91 (or 1 25/91 as a mixed number).

What is 3/7 plus 11/13 as a decimal?

3/7 + 11/13 converted to a decimal is 1.274725.

What is 3/7 plus 11/13 as a percentage?

3/7 + 11/13 expressed as a percentage is 127.4725%.

How do you write 3/7 plus 11/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 116/91 can be written as the mixed number 1 25/91.

Does 3/7 plus 11/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.274725...) because the denominator contains prime factors other than 2 and 5.