What is 1/13 plus 2/3? (Answer: 29/39)

Exact Answer

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Problem: What is 1/13 plus 2/3?
Formula / Expression: 1/13 + 2/3
Final Answer: 29/39
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 13 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 3 = 39.
Working: LCD(13, 3) = 39

Step 2: Convert to Equivalent Fractions with Common Denominator 39
Multiply the numerator and denominator of 1/13 by 3, and multiply the numerator and denominator of 2/3 by 13 so both fractions share the common base 39.
Working: 1 × 3/13 × 3 = 3/39 and 2 × 13/3 × 13 = 26/39

Step 3: Add the Numerators
Now add the numerators (3 + 26 = 29) and keep the common denominator 39 unchanged.
Working: 3 + 26/39 = 29/39

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 29 and 39 is 1, confirming that 29/39 cannot be reduced further—it is already in its simplest irreducible form.
Working: 29/39

Step 5: Decimal & Percentage Representation
Dividing the numerator 29 by denominator 39 produces a repeating decimal (approximately 0.74359, or 74.359%).
Working: 29 ÷ 39 = 0.74359 (74.359%)

Key Values:
- Simplified Fraction: 29/39
- Mixed Number Form: 29/39
- Decimal Value: 0.74359
- Percentage: 74.359%

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Solved with FractionsCalc:
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1/13 + 2/3 = 29/39

Simplified Fraction

29/39

Mixed Number

Proper (29/39)

Decimal Value

0.74359

Percentage

74.359%

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Step-by-Step Solution: 1/13 + 2/3

Step 1

Find the Least Common Denominator (LCD)

The denominators 13 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 3 = 39.

LCD(13, 3) = 39

Step 2

Convert to Equivalent Fractions with Common Denominator 39

Multiply the numerator and denominator of 1/13 by 3, and multiply the numerator and denominator of 2/3 by 13 so both fractions share the common base 39.

1 × 3/13 × 3 = 3/39 and 2 × 13/3 × 13 = 26/39

Step 3

Add the Numerators

Now add the numerators (3 + 26 = 29) and keep the common denominator 39 unchanged.

3 + 26/39 = 29/39

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 29 and 39 is 1, confirming that 29/39 cannot be reduced further—it is already in its simplest irreducible form.

29/39

Step 5

Decimal & Percentage Representation

Dividing the numerator 29 by denominator 39 produces a repeating decimal (approximately 0.74359, or 74.359%).

29 ÷ 39 = 0.74359 (74.359%)

Visual Representation

The diagram below illustrates 1/13 plus 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`29/39`
Mixed Number Form	`29/39`
Decimal Form	`0.74359`
Percentage	`74.359%`

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Frequently Asked Questions

What is 1/13 plus 2/3 as a fraction?

1/13 + 2/3 in simplest fraction form is 29/39.

What is 1/13 plus 2/3 as a decimal?

1/13 + 2/3 converted to a decimal is 0.74359.

What is 1/13 plus 2/3 as a percentage?

1/13 + 2/3 expressed as a percentage is 74.359%.

Does 1/13 plus 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.74359...) because the denominator contains prime factors other than 2 and 5.