What is 11/22 plus 7/13? (Answer: 27/26)

Exact Answer

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Problem: What is 11/22 plus 7/13?
Formula / Expression: 11/22 + 7/13
Final Answer: 1 1/26 (27/26)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 22 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 22 × 13 = 286.
Working: LCD(22, 13) = 286

Step 2: Convert to Equivalent Fractions with Common Denominator 286
Multiply the numerator and denominator of 11/22 by 13, and multiply the numerator and denominator of 7/13 by 22 so both fractions share the common base 286.
Working: 11 × 13/22 × 13 = 143/286 and 7 × 22/13 × 22 = 154/286

Step 3: Add the Numerators
Now add the numerators (143 + 154 = 297) and keep the common denominator 286 unchanged.
Working: 143 + 154/286 = 297/286

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 297 and 286, which is 11. Divide both the numerator and denominator by 11.
Working: 297 ÷ 11/286 ÷ 11 = 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:
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11/22 + 7/13 = 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: 11/22 + 7/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 22 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 22 × 13 = 286.

LCD(22, 13) = 286

Step 2

Convert to Equivalent Fractions with Common Denominator 286

Multiply the numerator and denominator of 11/22 by 13, and multiply the numerator and denominator of 7/13 by 22 so both fractions share the common base 286.

11 × 13/22 × 13 = 143/286 and 7 × 22/13 × 22 = 154/286

Step 3

Add the Numerators

Now add the numerators (143 + 154 = 297) and keep the common denominator 286 unchanged.

143 + 154/286 = 297/286

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 297 and 286, which is 11. Divide both the numerator and denominator by 11.

297 ÷ 11/286 ÷ 11 = 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 11/22 plus 7/13 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 11/22 plus 7/13 as a fraction?

11/22 + 7/13 in simplest fraction form is 27/26 (or 1 1/26 as a mixed number).

What is 11/22 plus 7/13 as a decimal?

11/22 + 7/13 converted to a decimal is 1.038462.

What is 11/22 plus 7/13 as a percentage?

11/22 + 7/13 expressed as a percentage is 103.8462%.

How do you write 11/22 plus 7/13 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 11/22 plus 7/13 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.