What is 3/34 plus 10/13? (Answer: 379/442)

Exact Answer

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Problem: What is 3/34 plus 10/13?
Formula / Expression: 3/34 + 10/13
Final Answer: 379/442
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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 3/34 by 13, and multiply the numerator and denominator of 10/13 by 34 so both fractions share the common base 442.
Working: 3 × 13/34 × 13 = 39/442 and 10 × 34/13 × 34 = 340/442

Step 3: Add the Numerators
Now add the numerators (39 + 340 = 379) and keep the common denominator 442 unchanged.
Working: 39 + 340/442 = 379/442

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 379 and 442 is 1, confirming that 379/442 cannot be reduced further—it is already in its simplest irreducible form.
Working: 379/442

Step 5: Decimal & Percentage Representation
Dividing the numerator 379 by denominator 442 produces a repeating decimal (approximately 0.857466, or 85.7466%).
Working: 379 ÷ 442 = 0.857466 (85.7466%)

Key Values:
- Simplified Fraction: 379/442
- Mixed Number Form: 379/442
- Decimal Value: 0.857466
- Percentage: 85.7466%

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Solved with FractionsCalc:
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3/34 + 10/13 = 379/442

Simplified Fraction

379/442

Mixed Number

Proper (379/442)

Decimal Value

0.857466

Percentage

85.7466%

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Step-by-Step Solution: 3/34 + 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 3/34 by 13, and multiply the numerator and denominator of 10/13 by 34 so both fractions share the common base 442.

3 × 13/34 × 13 = 39/442 and 10 × 34/13 × 34 = 340/442

Step 3

Add the Numerators

Now add the numerators (39 + 340 = 379) and keep the common denominator 442 unchanged.

39 + 340/442 = 379/442

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 379 and 442 is 1, confirming that 379/442 cannot be reduced further—it is already in its simplest irreducible form.

379/442

Step 5

Decimal & Percentage Representation

Dividing the numerator 379 by denominator 442 produces a repeating decimal (approximately 0.857466, or 85.7466%).

379 ÷ 442 = 0.857466 (85.7466%)

Visual Representation

The diagram below illustrates 3/34 plus 10/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`379/442`
Mixed Number Form	`379/442`
Decimal Form	`0.857466`
Percentage	`85.7466%`

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Frequently Asked Questions

What is 3/34 plus 10/13 as a fraction?

3/34 + 10/13 in simplest fraction form is 379/442.

What is 3/34 plus 10/13 as a decimal?

3/34 + 10/13 converted to a decimal is 0.857466.

What is 3/34 plus 10/13 as a percentage?

3/34 + 10/13 expressed as a percentage is 85.7466%.

Does 3/34 plus 10/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.857466...) because the denominator contains prime factors other than 2 and 5.