What is 17/34 plus 7/13? (Answer: 27/26)

Exact Answer

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Problem: What is 17/34 plus 7/13?
Formula / Expression: 17/34 + 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 34 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 34 × 13 = 442.
Working: LCD(34, 13) = 442

Step 2: Convert to Equivalent Fractions with Common Denominator 442
Multiply the numerator and denominator of 17/34 by 13, and multiply the numerator and denominator of 7/13 by 34 so both fractions share the common base 442.
Working: 17 × 13/34 × 13 = 221/442 and 7 × 34/13 × 34 = 238/442

Step 3: Add the Numerators
Now add the numerators (221 + 238 = 459) and keep the common denominator 442 unchanged.
Working: 221 + 238/442 = 459/442

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 459 and 442, which is 17. Divide both the numerator and denominator by 17.
Working: 459 ÷ 17/442 ÷ 17 = 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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17/34 + 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: 17/34 + 7/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 34 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 34 × 13 = 442.

LCD(34, 13) = 442

Step 2

Convert to Equivalent Fractions with Common Denominator 442

Multiply the numerator and denominator of 17/34 by 13, and multiply the numerator and denominator of 7/13 by 34 so both fractions share the common base 442.

17 × 13/34 × 13 = 221/442 and 7 × 34/13 × 34 = 238/442

Step 3

Add the Numerators

Now add the numerators (221 + 238 = 459) and keep the common denominator 442 unchanged.

221 + 238/442 = 459/442

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 459 and 442, which is 17. Divide both the numerator and denominator by 17.

459 ÷ 17/442 ÷ 17 = 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 17/34 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 17/34 plus 7/13 as a fraction?

17/34 + 7/13 in simplest fraction form is 27/26 (or 1 1/26 as a mixed number).

What is 17/34 plus 7/13 as a decimal?

17/34 + 7/13 converted to a decimal is 1.038462.

What is 17/34 plus 7/13 as a percentage?

17/34 + 7/13 expressed as a percentage is 103.8462%.

How do you write 17/34 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 17/34 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.