What is 6/8 plus 10/13? (Answer: 79/52)

Exact Answer

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Problem: What is 6/8 plus 10/13?
Formula / Expression: 6/8 + 10/13
Final Answer: 1 27/52 (79/52)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 8 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 8 × 13 = 104.
Working: LCD(8, 13) = 104

Step 2: Convert to Equivalent Fractions with Common Denominator 104
Multiply the numerator and denominator of 6/8 by 13, and multiply the numerator and denominator of 10/13 by 8 so both fractions share the common base 104.
Working: 6 × 13/8 × 13 = 78/104 and 10 × 8/13 × 8 = 80/104

Step 3: Add the Numerators
Now add the numerators (78 + 80 = 158) and keep the common denominator 104 unchanged.
Working: 78 + 80/104 = 158/104

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 158 and 104, which is 2. Divide both the numerator and denominator by 2.
Working: 158 ÷ 2/104 ÷ 2 = 79/52

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (79) is greater than the denominator (52), divide 79 by 52: it goes in 1 whole time(s) with a remainder of 27, giving the mixed number 1 27/52.
Working: 79/52 = 1 27/52

Step 6: Decimal & Percentage Representation
Dividing the numerator 79 by denominator 52 produces a repeating decimal (approximately 1.519231, or 151.9231%).
Working: 79 ÷ 52 = 1.519231 (151.9231%)

Key Values:
- Simplified Fraction: 79/52
- Mixed Number Form: 1 27/52
- Decimal Value: 1.519231
- Percentage: 151.9231%

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Solved with FractionsCalc:
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6/8 + 10/13 = 79/52

Simplified Fraction

79/52

Mixed Number

1 27/52

Decimal Value

1.519231

Percentage

151.9231%

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Step-by-Step Solution: 6/8 + 10/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 8 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 8 × 13 = 104.

LCD(8, 13) = 104

Step 2

Convert to Equivalent Fractions with Common Denominator 104

Multiply the numerator and denominator of 6/8 by 13, and multiply the numerator and denominator of 10/13 by 8 so both fractions share the common base 104.

6 × 13/8 × 13 = 78/104 and 10 × 8/13 × 8 = 80/104

Step 3

Add the Numerators

Now add the numerators (78 + 80 = 158) and keep the common denominator 104 unchanged.

78 + 80/104 = 158/104

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 158 and 104, which is 2. Divide both the numerator and denominator by 2.

158 ÷ 2/104 ÷ 2 = 79/52

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (79) is greater than the denominator (52), divide 79 by 52: it goes in 1 whole time(s) with a remainder of 27, giving the mixed number 1 27/52.

79/52 = 127/52

Step 6

Decimal & Percentage Representation

Dividing the numerator 79 by denominator 52 produces a repeating decimal (approximately 1.519231, or 151.9231%).

79 ÷ 52 = 1.519231 (151.9231%)

Visual Representation

The diagram below illustrates 6/8 plus 10/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`79/52`
Mixed Number Form	`1 27/52`
Decimal Form	`1.519231`
Percentage	`151.9231%`

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Frequently Asked Questions

What is 6/8 plus 10/13 as a fraction?

6/8 + 10/13 in simplest fraction form is 79/52 (or 1 27/52 as a mixed number).

What is 6/8 plus 10/13 as a decimal?

6/8 + 10/13 converted to a decimal is 1.519231.

What is 6/8 plus 10/13 as a percentage?

6/8 + 10/13 expressed as a percentage is 151.9231%.

How do you write 6/8 plus 10/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 79/52 can be written as the mixed number 1 27/52.

Does 6/8 plus 10/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.519231...) because the denominator contains prime factors other than 2 and 5.