What is 6/13 plus 3/6? (Answer: 25/26)

Exact Answer

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Problem: What is 6/13 plus 3/6?
Formula / Expression: 6/13 + 3/6
Final Answer: 25/26
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 13 and 6 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 6 = 78.
Working: LCD(13, 6) = 78

Step 2: Convert to Equivalent Fractions with Common Denominator 78
Multiply the numerator and denominator of 6/13 by 6, and multiply the numerator and denominator of 3/6 by 13 so both fractions share the common base 78.
Working: 6 × 6/13 × 6 = 36/78 and 3 × 13/6 × 13 = 39/78

Step 3: Add the Numerators
Now add the numerators (36 + 39 = 75) and keep the common denominator 78 unchanged.
Working: 36 + 39/78 = 75/78

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 75 and 78, which is 3. Divide both the numerator and denominator by 3.
Working: 75 ÷ 3/78 ÷ 3 = 25/26

Step 5: Decimal & Percentage Representation
Dividing the numerator 25 by denominator 26 produces a repeating decimal (approximately 0.961538, or 96.1538%).
Working: 25 ÷ 26 = 0.961538 (96.1538%)

Key Values:
- Simplified Fraction: 25/26
- Mixed Number Form: 25/26
- Decimal Value: 0.961538
- Percentage: 96.1538%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-6-13-plus-3-6/
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6/13 + 3/6 = 25/26

Simplified Fraction

25/26

Mixed Number

Proper (25/26)

Decimal Value

0.961538

Percentage

96.1538%

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Step-by-Step Solution: 6/13 + 3/6

Step 1

Find the Least Common Denominator (LCD)

The denominators 13 and 6 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 6 = 78.

LCD(13, 6) = 78

Step 2

Convert to Equivalent Fractions with Common Denominator 78

Multiply the numerator and denominator of 6/13 by 6, and multiply the numerator and denominator of 3/6 by 13 so both fractions share the common base 78.

6 × 6/13 × 6 = 36/78 and 3 × 13/6 × 13 = 39/78

Step 3

Add the Numerators

Now add the numerators (36 + 39 = 75) and keep the common denominator 78 unchanged.

36 + 39/78 = 75/78

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 75 and 78, which is 3. Divide both the numerator and denominator by 3.

75 ÷ 3/78 ÷ 3 = 25/26

Step 5

Decimal & Percentage Representation

Dividing the numerator 25 by denominator 26 produces a repeating decimal (approximately 0.961538, or 96.1538%).

25 ÷ 26 = 0.961538 (96.1538%)

Visual Representation

The diagram below illustrates 6/13 plus 3/6 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`25/26`
Mixed Number Form	`25/26`
Decimal Form	`0.961538`
Percentage	`96.1538%`

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Frequently Asked Questions

What is 6/13 plus 3/6 as a fraction?

6/13 + 3/6 in simplest fraction form is 25/26.

What is 6/13 plus 3/6 as a decimal?

6/13 + 3/6 converted to a decimal is 0.961538.

What is 6/13 plus 3/6 as a percentage?

6/13 + 3/6 expressed as a percentage is 96.1538%.

Does 6/13 plus 3/6 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.961538...) because the denominator contains prime factors other than 2 and 5.