What is 15/39 plus 9/13? (Answer: 14/13)

Exact Answer

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Problem: What is 15/39 plus 9/13?
Formula / Expression: 15/39 + 9/13
Final Answer: 1 1/13 (14/13)
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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(39, 13) = 39

Step 2: Convert to Equivalent Fractions with Common Denominator 39
Multiply the numerator and denominator of 15/39 by 1, and multiply the numerator and denominator of 9/13 by 3 so both fractions share the common base 39.
Working: 15 × 1/39 × 1 = 15/39 and 9 × 3/13 × 3 = 27/39

Step 3: Add the Numerators
Now add the numerators (15 + 27 = 42) and keep the common denominator 39 unchanged.
Working: 15 + 27/39 = 42/39

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 42 and 39, which is 3. Divide both the numerator and denominator by 3.
Working: 42 ÷ 3/39 ÷ 3 = 14/13

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (14) is greater than the denominator (13), divide 14 by 13: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/13.
Working: 14/13 = 1 1/13

Step 6: Decimal & Percentage Representation
Dividing the numerator 14 by denominator 13 produces a repeating decimal (approximately 1.076923, or 107.6923%).
Working: 14 ÷ 13 = 1.076923 (107.6923%)

Key Values:
- Simplified Fraction: 14/13
- Mixed Number Form: 1 1/13
- Decimal Value: 1.076923
- Percentage: 107.6923%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-15-39-plus-9-13/
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15/39 + 9/13 = 14/13

Simplified Fraction

14/13

Mixed Number

1 1/13

Decimal Value

1.076923

Percentage

107.6923%

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Step-by-Step Solution: 15/39 + 9/13

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(39, 13) = 39

Step 2

Convert to Equivalent Fractions with Common Denominator 39

Multiply the numerator and denominator of 15/39 by 1, and multiply the numerator and denominator of 9/13 by 3 so both fractions share the common base 39.

15 × 1/39 × 1 = 15/39 and 9 × 3/13 × 3 = 27/39

Step 3

Add the Numerators

Now add the numerators (15 + 27 = 42) and keep the common denominator 39 unchanged.

15 + 27/39 = 42/39

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 42 and 39, which is 3. Divide both the numerator and denominator by 3.

42 ÷ 3/39 ÷ 3 = 14/13

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (14) is greater than the denominator (13), divide 14 by 13: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/13.

14/13 = 11/13

Step 6

Decimal & Percentage Representation

Dividing the numerator 14 by denominator 13 produces a repeating decimal (approximately 1.076923, or 107.6923%).

14 ÷ 13 = 1.076923 (107.6923%)

Visual Representation

The diagram below illustrates 15/39 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`14/13`
Mixed Number Form	`1 1/13`
Decimal Form	`1.076923`
Percentage	`107.6923%`

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Frequently Asked Questions

What is 15/39 plus 9/13 as a fraction?

15/39 + 9/13 in simplest fraction form is 14/13 (or 1 1/13 as a mixed number).

What is 15/39 plus 9/13 as a decimal?

15/39 + 9/13 converted to a decimal is 1.076923.

What is 15/39 plus 9/13 as a percentage?

15/39 + 9/13 expressed as a percentage is 107.6923%.

How do you write 15/39 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 14/13 can be written as the mixed number 1 1/13.

Does 15/39 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.076923...) because the denominator contains prime factors other than 2 and 5.