What is 1/3 plus 8/13? (Answer: 37/39)

Exact Answer

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Problem: What is 1/3 plus 8/13?
Formula / Expression: 1/3 + 8/13
Final Answer: 37/39
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 39
Multiply the numerator and denominator of 1/3 by 13, and multiply the numerator and denominator of 8/13 by 3 so both fractions share the common base 39.
Working: 1 × 13/3 × 13 = 13/39 and 8 × 3/13 × 3 = 24/39

Step 3: Add the Numerators
Now add the numerators (13 + 24 = 37) and keep the common denominator 39 unchanged.
Working: 13 + 24/39 = 37/39

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 37 and 39 is 1, confirming that 37/39 cannot be reduced further—it is already in its simplest irreducible form.
Working: 37/39

Step 5: Decimal & Percentage Representation
Dividing the numerator 37 by denominator 39 produces a repeating decimal (approximately 0.948718, or 94.8718%).
Working: 37 ÷ 39 = 0.948718 (94.8718%)

Key Values:
- Simplified Fraction: 37/39
- Mixed Number Form: 37/39
- Decimal Value: 0.948718
- Percentage: 94.8718%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-3-plus-8-13/
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1/3 + 8/13 = 37/39

Simplified Fraction

37/39

Mixed Number

Proper (37/39)

Decimal Value

0.948718

Percentage

94.8718%

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Step-by-Step Solution: 1/3 + 8/13

Step 1

Find the Least Common Denominator (LCD)

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

LCD(3, 13) = 39

Step 2

Convert to Equivalent Fractions with Common Denominator 39

Multiply the numerator and denominator of 1/3 by 13, and multiply the numerator and denominator of 8/13 by 3 so both fractions share the common base 39.

1 × 13/3 × 13 = 13/39 and 8 × 3/13 × 3 = 24/39

Step 3

Add the Numerators

Now add the numerators (13 + 24 = 37) and keep the common denominator 39 unchanged.

13 + 24/39 = 37/39

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 37 and 39 is 1, confirming that 37/39 cannot be reduced further—it is already in its simplest irreducible form.

37/39

Step 5

Decimal & Percentage Representation

Dividing the numerator 37 by denominator 39 produces a repeating decimal (approximately 0.948718, or 94.8718%).

37 ÷ 39 = 0.948718 (94.8718%)

Visual Representation

The diagram below illustrates 1/3 plus 8/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`37/39`
Mixed Number Form	`37/39`
Decimal Form	`0.948718`
Percentage	`94.8718%`

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Frequently Asked Questions

What is 1/3 plus 8/13 as a fraction?

1/3 + 8/13 in simplest fraction form is 37/39.

What is 1/3 plus 8/13 as a decimal?

1/3 + 8/13 converted to a decimal is 0.948718.

What is 1/3 plus 8/13 as a percentage?

1/3 + 8/13 expressed as a percentage is 94.8718%.

Does 1/3 plus 8/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.948718...) because the denominator contains prime factors other than 2 and 5.