What is 3/34 plus 5/13? (Answer: 209/442)

Exact Answer

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Problem: What is 3/34 plus 5/13?
Formula / Expression: 3/34 + 5/13
Final Answer: 209/442
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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 5/13 by 34 so both fractions share the common base 442.
Working: 3 × 13/34 × 13 = 39/442 and 5 × 34/13 × 34 = 170/442

Step 3: Add the Numerators
Now add the numerators (39 + 170 = 209) and keep the common denominator 442 unchanged.
Working: 39 + 170/442 = 209/442

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 209 and 442 is 1, confirming that 209/442 cannot be reduced further—it is already in its simplest irreducible form.
Working: 209/442

Step 5: Decimal & Percentage Representation
Dividing the numerator 209 by denominator 442 produces a repeating decimal (approximately 0.472851, or 47.2851%).
Working: 209 ÷ 442 = 0.472851 (47.2851%)

Key Values:
- Simplified Fraction: 209/442
- Mixed Number Form: 209/442
- Decimal Value: 0.472851
- Percentage: 47.2851%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-34-plus-5-13/
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3/34 + 5/13 = 209/442

Simplified Fraction

209/442

Mixed Number

Proper (209/442)

Decimal Value

0.472851

Percentage

47.2851%

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Step-by-Step Solution: 3/34 + 5/13

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 5/13 by 34 so both fractions share the common base 442.

3 × 13/34 × 13 = 39/442 and 5 × 34/13 × 34 = 170/442

Step 3

Add the Numerators

Now add the numerators (39 + 170 = 209) and keep the common denominator 442 unchanged.

39 + 170/442 = 209/442

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 209 and 442 is 1, confirming that 209/442 cannot be reduced further—it is already in its simplest irreducible form.

209/442

Step 5

Decimal & Percentage Representation

Dividing the numerator 209 by denominator 442 produces a repeating decimal (approximately 0.472851, or 47.2851%).

209 ÷ 442 = 0.472851 (47.2851%)

Visual Representation

The diagram below illustrates 3/34 plus 5/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`209/442`
Mixed Number Form	`209/442`
Decimal Form	`0.472851`
Percentage	`47.2851%`

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Frequently Asked Questions

What is 3/34 plus 5/13 as a fraction?

3/34 + 5/13 in simplest fraction form is 209/442.

What is 3/34 plus 5/13 as a decimal?

3/34 + 5/13 converted to a decimal is 0.472851.

What is 3/34 plus 5/13 as a percentage?

3/34 + 5/13 expressed as a percentage is 47.2851%.

Does 3/34 plus 5/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.472851...) because the denominator contains prime factors other than 2 and 5.