What is 9/13 plus 27/39? (Answer: 18/13)

Exact Answer

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Problem: What is 9/13 plus 27/39?
Formula / Expression: 9/13 + 27/39
Final Answer: 1 5/13 (18/13)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 39 is an exact multiple of 13 (13 × 3 = 39). The Least Common Denominator (LCD) is simply 39, meaning we only need to scale one fraction.
Working: LCD(13, 39) = 39

Step 2: Convert to Equivalent Fractions with Common Denominator 39
Multiply the numerator and denominator of 9/13 by 3, and multiply the numerator and denominator of 27/39 by 1 so both fractions share the common base 39.
Working: 9 × 3/13 × 3 = 27/39 and 27 × 1/39 × 1 = 27/39

Step 3: Add the Numerators
Now add the numerators (27 + 27 = 54) and keep the common denominator 39 unchanged.
Working: 27 + 27/39 = 54/39

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 54 and 39, which is 3. Divide both the numerator and denominator by 3.
Working: 54 ÷ 3/39 ÷ 3 = 18/13

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (18) is greater than the denominator (13), divide 18 by 13: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/13.
Working: 18/13 = 1 5/13

Step 6: Decimal & Percentage Representation
Dividing the numerator 18 by denominator 13 produces a repeating decimal (approximately 1.384615, or 138.4615%).
Working: 18 ÷ 13 = 1.384615 (138.4615%)

Key Values:
- Simplified Fraction: 18/13
- Mixed Number Form: 1 5/13
- Decimal Value: 1.384615
- Percentage: 138.4615%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-9-13-plus-27-39/
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9/13 + 27/39 = 18/13

Simplified Fraction

18/13

Mixed Number

1 5/13

Decimal Value

1.384615

Percentage

138.4615%

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Step-by-Step Solution: 9/13 + 27/39

Step 1

Find the Least Common Denominator (LCD)

Notice that 39 is an exact multiple of 13 (13 × 3 = 39). The Least Common Denominator (LCD) is simply 39, meaning we only need to scale one fraction.

LCD(13, 39) = 39

Step 2

Convert to Equivalent Fractions with Common Denominator 39

Multiply the numerator and denominator of 9/13 by 3, and multiply the numerator and denominator of 27/39 by 1 so both fractions share the common base 39.

9 × 3/13 × 3 = 27/39 and 27 × 1/39 × 1 = 27/39

Step 3

Add the Numerators

Now add the numerators (27 + 27 = 54) and keep the common denominator 39 unchanged.

27 + 27/39 = 54/39

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 54 and 39, which is 3. Divide both the numerator and denominator by 3.

54 ÷ 3/39 ÷ 3 = 18/13

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (18) is greater than the denominator (13), divide 18 by 13: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/13.

18/13 = 15/13

Step 6

Decimal & Percentage Representation

Dividing the numerator 18 by denominator 13 produces a repeating decimal (approximately 1.384615, or 138.4615%).

18 ÷ 13 = 1.384615 (138.4615%)

Visual Representation

The diagram below illustrates 9/13 plus 27/39 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`18/13`
Mixed Number Form	`1 5/13`
Decimal Form	`1.384615`
Percentage	`138.4615%`

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Frequently Asked Questions

What is 9/13 plus 27/39 as a fraction?

9/13 + 27/39 in simplest fraction form is 18/13 (or 1 5/13 as a mixed number).

What is 9/13 plus 27/39 as a decimal?

9/13 + 27/39 converted to a decimal is 1.384615.

What is 9/13 plus 27/39 as a percentage?

9/13 + 27/39 expressed as a percentage is 138.4615%.

How do you write 9/13 plus 27/39 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 18/13 can be written as the mixed number 1 5/13.

Does 9/13 plus 27/39 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.384615...) because the denominator contains prime factors other than 2 and 5.