What is 9/34 plus 10/13? (Answer: 457/442)

Exact Answer

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Problem: What is 9/34 plus 10/13?
Formula / Expression: 9/34 + 10/13
Final Answer: 1 15/442 (457/442)
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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 9/34 by 13, and multiply the numerator and denominator of 10/13 by 34 so both fractions share the common base 442.
Working: 9 × 13/34 × 13 = 117/442 and 10 × 34/13 × 34 = 340/442

Step 3: Add the Numerators
Now add the numerators (117 + 340 = 457) and keep the common denominator 442 unchanged.
Working: 117 + 340/442 = 457/442

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 457 and 442 is 1, confirming that 457/442 cannot be reduced further—it is already in its simplest irreducible form.
Working: 457/442

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (457) is greater than the denominator (442), divide 457 by 442: it goes in 1 whole time(s) with a remainder of 15, giving the mixed number 1 15/442.
Working: 457/442 = 1 15/442

Step 6: Decimal & Percentage Representation
Dividing the numerator 457 by denominator 442 produces a repeating decimal (approximately 1.033937, or 103.3937%).
Working: 457 ÷ 442 = 1.033937 (103.3937%)

Key Values:
- Simplified Fraction: 457/442
- Mixed Number Form: 1 15/442
- Decimal Value: 1.033937
- Percentage: 103.3937%

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Solved with FractionsCalc:
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9/34 + 10/13 = 457/442

Simplified Fraction

457/442

Mixed Number

1 15/442

Decimal Value

1.033937

Percentage

103.3937%

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Step-by-Step Solution: 9/34 + 10/13

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 9/34 by 13, and multiply the numerator and denominator of 10/13 by 34 so both fractions share the common base 442.

9 × 13/34 × 13 = 117/442 and 10 × 34/13 × 34 = 340/442

Step 3

Add the Numerators

Now add the numerators (117 + 340 = 457) and keep the common denominator 442 unchanged.

117 + 340/442 = 457/442

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 457 and 442 is 1, confirming that 457/442 cannot be reduced further—it is already in its simplest irreducible form.

457/442

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (457) is greater than the denominator (442), divide 457 by 442: it goes in 1 whole time(s) with a remainder of 15, giving the mixed number 1 15/442.

457/442 = 115/442

Step 6

Decimal & Percentage Representation

Dividing the numerator 457 by denominator 442 produces a repeating decimal (approximately 1.033937, or 103.3937%).

457 ÷ 442 = 1.033937 (103.3937%)

Visual Representation

The diagram below illustrates 9/34 plus 10/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`457/442`
Mixed Number Form	`1 15/442`
Decimal Form	`1.033937`
Percentage	`103.3937%`

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Frequently Asked Questions

What is 9/34 plus 10/13 as a fraction?

9/34 + 10/13 in simplest fraction form is 457/442 (or 1 15/442 as a mixed number).

What is 9/34 plus 10/13 as a decimal?

9/34 + 10/13 converted to a decimal is 1.033937.

What is 9/34 plus 10/13 as a percentage?

9/34 + 10/13 expressed as a percentage is 103.3937%.

How do you write 9/34 plus 10/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 457/442 can be written as the mixed number 1 15/442.

Does 9/34 plus 10/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.033937...) because the denominator contains prime factors other than 2 and 5.