What is 13/34 plus 7/13? (Answer: 407/442)

Exact Answer

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Problem: What is 13/34 plus 7/13?
Formula / Expression: 13/34 + 7/13
Final Answer: 407/442
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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 13/34 by 13, and multiply the numerator and denominator of 7/13 by 34 so both fractions share the common base 442.
Working: 13 × 13/34 × 13 = 169/442 and 7 × 34/13 × 34 = 238/442

Step 3: Add the Numerators
Now add the numerators (169 + 238 = 407) and keep the common denominator 442 unchanged.
Working: 169 + 238/442 = 407/442

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 407 and 442 is 1, confirming that 407/442 cannot be reduced further—it is already in its simplest irreducible form.
Working: 407/442

Step 5: Decimal & Percentage Representation
Dividing the numerator 407 by denominator 442 produces a repeating decimal (approximately 0.920814, or 92.0814%).
Working: 407 ÷ 442 = 0.920814 (92.0814%)

Key Values:
- Simplified Fraction: 407/442
- Mixed Number Form: 407/442
- Decimal Value: 0.920814
- Percentage: 92.0814%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-13-34-plus-7-13/
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13/34 + 7/13 = 407/442

Simplified Fraction

407/442

Mixed Number

Proper (407/442)

Decimal Value

0.920814

Percentage

92.0814%

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Step-by-Step Solution: 13/34 + 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 13/34 by 13, and multiply the numerator and denominator of 7/13 by 34 so both fractions share the common base 442.

13 × 13/34 × 13 = 169/442 and 7 × 34/13 × 34 = 238/442

Step 3

Add the Numerators

Now add the numerators (169 + 238 = 407) and keep the common denominator 442 unchanged.

169 + 238/442 = 407/442

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 407 and 442 is 1, confirming that 407/442 cannot be reduced further—it is already in its simplest irreducible form.

407/442

Step 5

Decimal & Percentage Representation

Dividing the numerator 407 by denominator 442 produces a repeating decimal (approximately 0.920814, or 92.0814%).

407 ÷ 442 = 0.920814 (92.0814%)

Visual Representation

The diagram below illustrates 13/34 plus 7/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`407/442`
Mixed Number Form	`407/442`
Decimal Form	`0.920814`
Percentage	`92.0814%`

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Frequently Asked Questions

What is 13/34 plus 7/13 as a fraction?

13/34 + 7/13 in simplest fraction form is 407/442.

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

13/34 + 7/13 converted to a decimal is 0.920814.

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

13/34 + 7/13 expressed as a percentage is 92.0814%.

Does 13/34 plus 7/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.920814...) because the denominator contains prime factors other than 2 and 5.