What is 2/7 plus 10/13? (Answer: 96/91)

Exact Answer

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Problem: What is 2/7 plus 10/13?
Formula / Expression: 2/7 + 10/13
Final Answer: 1 5/91 (96/91)
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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 10/13 by 7 so both fractions share the common base 91.
Working: 2 × 13/7 × 13 = 26/91 and 10 × 7/13 × 7 = 70/91

Step 3: Add the Numerators
Now add the numerators (26 + 70 = 96) and keep the common denominator 91 unchanged.
Working: 26 + 70/91 = 96/91

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 96 and 91 is 1, confirming that 96/91 cannot be reduced further—it is already in its simplest irreducible form.
Working: 96/91

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (96) is greater than the denominator (91), divide 96 by 91: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/91.
Working: 96/91 = 1 5/91

Step 6: Decimal & Percentage Representation
Dividing the numerator 96 by denominator 91 produces a repeating decimal (approximately 1.054945, or 105.4945%).
Working: 96 ÷ 91 = 1.054945 (105.4945%)

Key Values:
- Simplified Fraction: 96/91
- Mixed Number Form: 1 5/91
- Decimal Value: 1.054945
- Percentage: 105.4945%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-7-plus-10-13/
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2/7 + 10/13 = 96/91

Simplified Fraction

96/91

Mixed Number

1 5/91

Decimal Value

1.054945

Percentage

105.4945%

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Step-by-Step Solution: 2/7 + 10/13

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 10/13 by 7 so both fractions share the common base 91.

2 × 13/7 × 13 = 26/91 and 10 × 7/13 × 7 = 70/91

Step 3

Add the Numerators

Now add the numerators (26 + 70 = 96) and keep the common denominator 91 unchanged.

26 + 70/91 = 96/91

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 96 and 91 is 1, confirming that 96/91 cannot be reduced further—it is already in its simplest irreducible form.

96/91

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (96) is greater than the denominator (91), divide 96 by 91: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/91.

96/91 = 15/91

Step 6

Decimal & Percentage Representation

Dividing the numerator 96 by denominator 91 produces a repeating decimal (approximately 1.054945, or 105.4945%).

96 ÷ 91 = 1.054945 (105.4945%)

Visual Representation

The diagram below illustrates 2/7 plus 10/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`96/91`
Mixed Number Form	`1 5/91`
Decimal Form	`1.054945`
Percentage	`105.4945%`

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Frequently Asked Questions

What is 2/7 plus 10/13 as a fraction?

2/7 + 10/13 in simplest fraction form is 96/91 (or 1 5/91 as a mixed number).

What is 2/7 plus 10/13 as a decimal?

2/7 + 10/13 converted to a decimal is 1.054945.

What is 2/7 plus 10/13 as a percentage?

2/7 + 10/13 expressed as a percentage is 105.4945%.

How do you write 2/7 plus 10/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 96/91 can be written as the mixed number 1 5/91.

Does 2/7 plus 10/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.054945...) because the denominator contains prime factors other than 2 and 5.