What is 1/6 plus 7/13? (Answer: 55/78)

Exact Answer

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Problem: What is 1/6 plus 7/13?
Formula / Expression: 1/6 + 7/13
Final Answer: 55/78
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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 7/13 by 6 so both fractions share the common base 78.
Working: 1 × 13/6 × 13 = 13/78 and 7 × 6/13 × 6 = 42/78

Step 3: Add the Numerators
Now add the numerators (13 + 42 = 55) and keep the common denominator 78 unchanged.
Working: 13 + 42/78 = 55/78

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 55 and 78 is 1, confirming that 55/78 cannot be reduced further—it is already in its simplest irreducible form.
Working: 55/78

Step 5: Decimal & Percentage Representation
Dividing the numerator 55 by denominator 78 produces a repeating decimal (approximately 0.705128, or 70.5128%).
Working: 55 ÷ 78 = 0.705128 (70.5128%)

Key Values:
- Simplified Fraction: 55/78
- Mixed Number Form: 55/78
- Decimal Value: 0.705128
- Percentage: 70.5128%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-6-plus-7-13/
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1/6 + 7/13 = 55/78

Simplified Fraction

55/78

Mixed Number

Proper (55/78)

Decimal Value

0.705128

Percentage

70.5128%

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Step-by-Step Solution: 1/6 + 7/13

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 7/13 by 6 so both fractions share the common base 78.

1 × 13/6 × 13 = 13/78 and 7 × 6/13 × 6 = 42/78

Step 3

Add the Numerators

Now add the numerators (13 + 42 = 55) and keep the common denominator 78 unchanged.

13 + 42/78 = 55/78

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 55 and 78 is 1, confirming that 55/78 cannot be reduced further—it is already in its simplest irreducible form.

55/78

Step 5

Decimal & Percentage Representation

Dividing the numerator 55 by denominator 78 produces a repeating decimal (approximately 0.705128, or 70.5128%).

55 ÷ 78 = 0.705128 (70.5128%)

Visual Representation

The diagram below illustrates 1/6 plus 7/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`55/78`
Mixed Number Form	`55/78`
Decimal Form	`0.705128`
Percentage	`70.5128%`

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Frequently Asked Questions

What is 1/6 plus 7/13 as a fraction?

1/6 + 7/13 in simplest fraction form is 55/78.

What is 1/6 plus 7/13 as a decimal?

1/6 + 7/13 converted to a decimal is 0.705128.

What is 1/6 plus 7/13 as a percentage?

1/6 + 7/13 expressed as a percentage is 70.5128%.

Does 1/6 plus 7/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.705128...) because the denominator contains prime factors other than 2 and 5.