What is 9/39 plus 9/13? (Answer: 12/13)

Exact Answer

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Problem: What is 9/39 plus 9/13?
Formula / Expression: 9/39 + 9/13
Final Answer: 12/13
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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 9/39 by 1, and multiply the numerator and denominator of 9/13 by 3 so both fractions share the common base 39.
Working: 9 × 1/39 × 1 = 9/39 and 9 × 3/13 × 3 = 27/39

Step 3: Add the Numerators
Now add the numerators (9 + 27 = 36) and keep the common denominator 39 unchanged.
Working: 9 + 27/39 = 36/39

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 36 and 39, which is 3. Divide both the numerator and denominator by 3.
Working: 36 ÷ 3/39 ÷ 3 = 12/13

Step 5: Decimal & Percentage Representation
Dividing the numerator 12 by denominator 13 produces a repeating decimal (approximately 0.923077, or 92.3077%).
Working: 12 ÷ 13 = 0.923077 (92.3077%)

Key Values:
- Simplified Fraction: 12/13
- Mixed Number Form: 12/13
- Decimal Value: 0.923077
- Percentage: 92.3077%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-9-39-plus-9-13/
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9/39 + 9/13 = 12/13

Simplified Fraction

12/13

Mixed Number

Proper (12/13)

Decimal Value

0.923077

Percentage

92.3077%

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Step-by-Step Solution: 9/39 + 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 9/39 by 1, and multiply the numerator and denominator of 9/13 by 3 so both fractions share the common base 39.

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

Step 3

Add the Numerators

Now add the numerators (9 + 27 = 36) and keep the common denominator 39 unchanged.

9 + 27/39 = 36/39

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 36 and 39, which is 3. Divide both the numerator and denominator by 3.

36 ÷ 3/39 ÷ 3 = 12/13

Step 5

Decimal & Percentage Representation

Dividing the numerator 12 by denominator 13 produces a repeating decimal (approximately 0.923077, or 92.3077%).

12 ÷ 13 = 0.923077 (92.3077%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`12/13`
Mixed Number Form	`12/13`
Decimal Form	`0.923077`
Percentage	`92.3077%`

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Frequently Asked Questions

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

9/39 + 9/13 in simplest fraction form is 12/13.

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

9/39 + 9/13 converted to a decimal is 0.923077.

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

9/39 + 9/13 expressed as a percentage is 92.3077%.

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

It results in a repeating decimal (approximately 0.923077...) because the denominator contains prime factors other than 2 and 5.