What is 7/26 plus 10/13? (Answer: 27/26)

Exact Answer

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Problem: What is 7/26 plus 10/13?
Formula / Expression: 7/26 + 10/13
Final Answer: 1 1/26 (27/26)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 26 is an exact multiple of 13 (13 × 2 = 26). The Least Common Denominator (LCD) is simply 26, meaning we only need to scale one fraction.
Working: LCD(26, 13) = 26

Step 2: Convert to Equivalent Fractions with Common Denominator 26
Multiply the numerator and denominator of 7/26 by 1, and multiply the numerator and denominator of 10/13 by 2 so both fractions share the common base 26.
Working: 7 × 1/26 × 1 = 7/26 and 10 × 2/13 × 2 = 20/26

Step 3: Add the Numerators
Now add the numerators (7 + 20 = 27) and keep the common denominator 26 unchanged.
Working: 7 + 20/26 = 27/26

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 27 and 26 is 1, confirming that 27/26 cannot be reduced further—it is already in its simplest irreducible form.
Working: 27/26

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (27) is greater than the denominator (26), divide 27 by 26: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/26.
Working: 27/26 = 1 1/26

Step 6: Decimal & Percentage Representation
Dividing the numerator 27 by denominator 26 produces a repeating decimal (approximately 1.038462, or 103.8462%).
Working: 27 ÷ 26 = 1.038462 (103.8462%)

Key Values:
- Simplified Fraction: 27/26
- Mixed Number Form: 1 1/26
- Decimal Value: 1.038462
- Percentage: 103.8462%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-7-26-plus-10-13/
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7/26 + 10/13 = 27/26

Simplified Fraction

27/26

Mixed Number

1 1/26

Decimal Value

1.038462

Percentage

103.8462%

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Step-by-Step Solution: 7/26 + 10/13

Step 1

Find the Least Common Denominator (LCD)

Notice that 26 is an exact multiple of 13 (13 × 2 = 26). The Least Common Denominator (LCD) is simply 26, meaning we only need to scale one fraction.

LCD(26, 13) = 26

Step 2

Convert to Equivalent Fractions with Common Denominator 26

Multiply the numerator and denominator of 7/26 by 1, and multiply the numerator and denominator of 10/13 by 2 so both fractions share the common base 26.

7 × 1/26 × 1 = 7/26 and 10 × 2/13 × 2 = 20/26

Step 3

Add the Numerators

Now add the numerators (7 + 20 = 27) and keep the common denominator 26 unchanged.

7 + 20/26 = 27/26

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 27 and 26 is 1, confirming that 27/26 cannot be reduced further—it is already in its simplest irreducible form.

27/26

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (27) is greater than the denominator (26), divide 27 by 26: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/26.

27/26 = 11/26

Step 6

Decimal & Percentage Representation

Dividing the numerator 27 by denominator 26 produces a repeating decimal (approximately 1.038462, or 103.8462%).

27 ÷ 26 = 1.038462 (103.8462%)

Visual Representation

The diagram below illustrates 7/26 plus 10/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`27/26`
Mixed Number Form	`1 1/26`
Decimal Form	`1.038462`
Percentage	`103.8462%`

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Frequently Asked Questions

What is 7/26 plus 10/13 as a fraction?

7/26 + 10/13 in simplest fraction form is 27/26 (or 1 1/26 as a mixed number).

What is 7/26 plus 10/13 as a decimal?

7/26 + 10/13 converted to a decimal is 1.038462.

What is 7/26 plus 10/13 as a percentage?

7/26 + 10/13 expressed as a percentage is 103.8462%.

How do you write 7/26 plus 10/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 27/26 can be written as the mixed number 1 1/26.

Does 7/26 plus 10/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.038462...) because the denominator contains prime factors other than 2 and 5.