What is 6/9 plus 10/13? (Answer: 56/39)

Exact Answer

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Problem: What is 6/9 plus 10/13?
Formula / Expression: 6/9 + 10/13
Final Answer: 1 17/39 (56/39)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 13 = 117.
Working: LCD(9, 13) = 117

Step 2: Convert to Equivalent Fractions with Common Denominator 117
Multiply the numerator and denominator of 6/9 by 13, and multiply the numerator and denominator of 10/13 by 9 so both fractions share the common base 117.
Working: 6 × 13/9 × 13 = 78/117 and 10 × 9/13 × 9 = 90/117

Step 3: Add the Numerators
Now add the numerators (78 + 90 = 168) and keep the common denominator 117 unchanged.
Working: 78 + 90/117 = 168/117

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 168 and 117, which is 3. Divide both the numerator and denominator by 3.
Working: 168 ÷ 3/117 ÷ 3 = 56/39

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (56) is greater than the denominator (39), divide 56 by 39: it goes in 1 whole time(s) with a remainder of 17, giving the mixed number 1 17/39.
Working: 56/39 = 1 17/39

Step 6: Decimal & Percentage Representation
Dividing the numerator 56 by denominator 39 produces a repeating decimal (approximately 1.435897, or 143.5897%).
Working: 56 ÷ 39 = 1.435897 (143.5897%)

Key Values:
- Simplified Fraction: 56/39
- Mixed Number Form: 1 17/39
- Decimal Value: 1.435897
- Percentage: 143.5897%

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Solved with FractionsCalc:
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6/9 + 10/13 = 56/39

Simplified Fraction

56/39

Mixed Number

1 17/39

Decimal Value

1.435897

Percentage

143.5897%

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Step-by-Step Solution: 6/9 + 10/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 13 = 117.

LCD(9, 13) = 117

Step 2

Convert to Equivalent Fractions with Common Denominator 117

Multiply the numerator and denominator of 6/9 by 13, and multiply the numerator and denominator of 10/13 by 9 so both fractions share the common base 117.

6 × 13/9 × 13 = 78/117 and 10 × 9/13 × 9 = 90/117

Step 3

Add the Numerators

Now add the numerators (78 + 90 = 168) and keep the common denominator 117 unchanged.

78 + 90/117 = 168/117

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 168 and 117, which is 3. Divide both the numerator and denominator by 3.

168 ÷ 3/117 ÷ 3 = 56/39

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (56) is greater than the denominator (39), divide 56 by 39: it goes in 1 whole time(s) with a remainder of 17, giving the mixed number 1 17/39.

56/39 = 117/39

Step 6

Decimal & Percentage Representation

Dividing the numerator 56 by denominator 39 produces a repeating decimal (approximately 1.435897, or 143.5897%).

56 ÷ 39 = 1.435897 (143.5897%)

Visual Representation

The diagram below illustrates 6/9 plus 10/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`56/39`
Mixed Number Form	`1 17/39`
Decimal Form	`1.435897`
Percentage	`143.5897%`

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Frequently Asked Questions

What is 6/9 plus 10/13 as a fraction?

6/9 + 10/13 in simplest fraction form is 56/39 (or 1 17/39 as a mixed number).

What is 6/9 plus 10/13 as a decimal?

6/9 + 10/13 converted to a decimal is 1.435897.

What is 6/9 plus 10/13 as a percentage?

6/9 + 10/13 expressed as a percentage is 143.5897%.

How do you write 6/9 plus 10/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 56/39 can be written as the mixed number 1 17/39.

Does 6/9 plus 10/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.435897...) because the denominator contains prime factors other than 2 and 5.