What is 3/14 plus 5/13? (Answer: 109/182)

Exact Answer

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Problem: What is 3/14 plus 5/13?
Formula / Expression: 3/14 + 5/13
Final Answer: 109/182
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 14 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 14 × 13 = 182.
Working: LCD(14, 13) = 182

Step 2: Convert to Equivalent Fractions with Common Denominator 182
Multiply the numerator and denominator of 3/14 by 13, and multiply the numerator and denominator of 5/13 by 14 so both fractions share the common base 182.
Working: 3 × 13/14 × 13 = 39/182 and 5 × 14/13 × 14 = 70/182

Step 3: Add the Numerators
Now add the numerators (39 + 70 = 109) and keep the common denominator 182 unchanged.
Working: 39 + 70/182 = 109/182

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 109 and 182 is 1, confirming that 109/182 cannot be reduced further—it is already in its simplest irreducible form.
Working: 109/182

Step 5: Decimal & Percentage Representation
Dividing the numerator 109 by denominator 182 produces a repeating decimal (approximately 0.598901, or 59.8901%).
Working: 109 ÷ 182 = 0.598901 (59.8901%)

Key Values:
- Simplified Fraction: 109/182
- Mixed Number Form: 109/182
- Decimal Value: 0.598901
- Percentage: 59.8901%

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Solved with FractionsCalc:
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3/14 + 5/13 = 109/182

Simplified Fraction

109/182

Mixed Number

Proper (109/182)

Decimal Value

0.598901

Percentage

59.8901%

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Step-by-Step Solution: 3/14 + 5/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 14 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 14 × 13 = 182.

LCD(14, 13) = 182

Step 2

Convert to Equivalent Fractions with Common Denominator 182

Multiply the numerator and denominator of 3/14 by 13, and multiply the numerator and denominator of 5/13 by 14 so both fractions share the common base 182.

3 × 13/14 × 13 = 39/182 and 5 × 14/13 × 14 = 70/182

Step 3

Add the Numerators

Now add the numerators (39 + 70 = 109) and keep the common denominator 182 unchanged.

39 + 70/182 = 109/182

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 109 and 182 is 1, confirming that 109/182 cannot be reduced further—it is already in its simplest irreducible form.

109/182

Step 5

Decimal & Percentage Representation

Dividing the numerator 109 by denominator 182 produces a repeating decimal (approximately 0.598901, or 59.8901%).

109 ÷ 182 = 0.598901 (59.8901%)

Visual Representation

The diagram below illustrates 3/14 plus 5/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`109/182`
Mixed Number Form	`109/182`
Decimal Form	`0.598901`
Percentage	`59.8901%`

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Frequently Asked Questions

What is 3/14 plus 5/13 as a fraction?

3/14 + 5/13 in simplest fraction form is 109/182.

What is 3/14 plus 5/13 as a decimal?

3/14 + 5/13 converted to a decimal is 0.598901.

What is 3/14 plus 5/13 as a percentage?

3/14 + 5/13 expressed as a percentage is 59.8901%.

Does 3/14 plus 5/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.598901...) because the denominator contains prime factors other than 2 and 5.