What is 3/13 plus 9/39? (Answer: 6/13)

Exact Answer

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Problem: What is 3/13 plus 9/39?
Formula / Expression: 3/13 + 9/39
Final Answer: 6/13
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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 3/13 by 3, and multiply the numerator and denominator of 9/39 by 1 so both fractions share the common base 39.
Working: 3 × 3/13 × 3 = 9/39 and 9 × 1/39 × 1 = 9/39

Step 3: Add the Numerators
Now add the numerators (9 + 9 = 18) and keep the common denominator 39 unchanged.
Working: 9 + 9/39 = 18/39

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 18 and 39, which is 3. Divide both the numerator and denominator by 3.
Working: 18 ÷ 3/39 ÷ 3 = 6/13

Step 5: Decimal & Percentage Representation
Dividing the numerator 6 by denominator 13 produces a repeating decimal (approximately 0.461538, or 46.1538%).
Working: 6 ÷ 13 = 0.461538 (46.1538%)

Key Values:
- Simplified Fraction: 6/13
- Mixed Number Form: 6/13
- Decimal Value: 0.461538
- Percentage: 46.1538%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-13-plus-9-39/
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3/13 + 9/39 = 6/13

Simplified Fraction

6/13

Mixed Number

Proper (6/13)

Decimal Value

0.461538

Percentage

46.1538%

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Step-by-Step Solution: 3/13 + 9/39

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

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

Step 3

Add the Numerators

Now add the numerators (9 + 9 = 18) and keep the common denominator 39 unchanged.

9 + 9/39 = 18/39

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 18 and 39, which is 3. Divide both the numerator and denominator by 3.

18 ÷ 3/39 ÷ 3 = 6/13

Step 5

Decimal & Percentage Representation

Dividing the numerator 6 by denominator 13 produces a repeating decimal (approximately 0.461538, or 46.1538%).

6 ÷ 13 = 0.461538 (46.1538%)

Visual Representation

The diagram below illustrates 3/13 plus 9/39 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`6/13`
Mixed Number Form	`6/13`
Decimal Form	`0.461538`
Percentage	`46.1538%`

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Frequently Asked Questions

What is 3/13 plus 9/39 as a fraction?

3/13 + 9/39 in simplest fraction form is 6/13.

What is 3/13 plus 9/39 as a decimal?

3/13 + 9/39 converted to a decimal is 0.461538.

What is 3/13 plus 9/39 as a percentage?

3/13 + 9/39 expressed as a percentage is 46.1538%.

Does 3/13 plus 9/39 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.461538...) because the denominator contains prime factors other than 2 and 5.