What is 1/6 plus 6/13? (Answer: 49/78)

Exact Answer

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Problem: What is 1/6 plus 6/13?
Formula / Expression: 1/6 + 6/13
Final Answer: 49/78
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 78
Multiply the numerator and denominator of 1/6 by 13, and multiply the numerator and denominator of 6/13 by 6 so both fractions share the common base 78.
Working: 1 × 13/6 × 13 = 13/78 and 6 × 6/13 × 6 = 36/78

Step 3: Add the Numerators
Now add the numerators (13 + 36 = 49) and keep the common denominator 78 unchanged.
Working: 13 + 36/78 = 49/78

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 49 and 78 is 1, confirming that 49/78 cannot be reduced further—it is already in its simplest irreducible form.
Working: 49/78

Step 5: Decimal & Percentage Representation
Dividing the numerator 49 by denominator 78 produces a repeating decimal (approximately 0.628205, or 62.8205%).
Working: 49 ÷ 78 = 0.628205 (62.8205%)

Key Values:
- Simplified Fraction: 49/78
- Mixed Number Form: 49/78
- Decimal Value: 0.628205
- Percentage: 62.8205%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-6-plus-6-13/
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1/6 + 6/13 = 49/78

Simplified Fraction

49/78

Mixed Number

Proper (49/78)

Decimal Value

0.628205

Percentage

62.8205%

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Step-by-Step Solution: 1/6 + 6/13

Step 1

Find the Least Common Denominator (LCD)

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

LCD(6, 13) = 78

Step 2

Convert to Equivalent Fractions with Common Denominator 78

Multiply the numerator and denominator of 1/6 by 13, and multiply the numerator and denominator of 6/13 by 6 so both fractions share the common base 78.

1 × 13/6 × 13 = 13/78 and 6 × 6/13 × 6 = 36/78

Step 3

Add the Numerators

Now add the numerators (13 + 36 = 49) and keep the common denominator 78 unchanged.

13 + 36/78 = 49/78

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 49 and 78 is 1, confirming that 49/78 cannot be reduced further—it is already in its simplest irreducible form.

49/78

Step 5

Decimal & Percentage Representation

Dividing the numerator 49 by denominator 78 produces a repeating decimal (approximately 0.628205, or 62.8205%).

49 ÷ 78 = 0.628205 (62.8205%)

Visual Representation

The diagram below illustrates 1/6 plus 6/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`49/78`
Mixed Number Form	`49/78`
Decimal Form	`0.628205`
Percentage	`62.8205%`

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Frequently Asked Questions

What is 1/6 plus 6/13 as a fraction?

1/6 + 6/13 in simplest fraction form is 49/78.

What is 1/6 plus 6/13 as a decimal?

1/6 + 6/13 converted to a decimal is 0.628205.

What is 1/6 plus 6/13 as a percentage?

1/6 + 6/13 expressed as a percentage is 62.8205%.

Does 1/6 plus 6/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.628205...) because the denominator contains prime factors other than 2 and 5.