What is 4/13 plus 12/39? (Answer: 8/13)

Exact Answer

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Problem: What is 4/13 plus 12/39?
Formula / Expression: 4/13 + 12/39
Final Answer: 8/13
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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 4/13 by 3, and multiply the numerator and denominator of 12/39 by 1 so both fractions share the common base 39.
Working: 4 × 3/13 × 3 = 12/39 and 12 × 1/39 × 1 = 12/39

Step 3: Add the Numerators
Now add the numerators (12 + 12 = 24) and keep the common denominator 39 unchanged.
Working: 12 + 12/39 = 24/39

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 24 and 39, which is 3. Divide both the numerator and denominator by 3.
Working: 24 ÷ 3/39 ÷ 3 = 8/13

Step 5: Decimal & Percentage Representation
Dividing the numerator 8 by denominator 13 produces a repeating decimal (approximately 0.615385, or 61.5385%).
Working: 8 ÷ 13 = 0.615385 (61.5385%)

Key Values:
- Simplified Fraction: 8/13
- Mixed Number Form: 8/13
- Decimal Value: 0.615385
- Percentage: 61.5385%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-13-plus-12-39/
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4/13 + 12/39 = 8/13

Simplified Fraction

8/13

Mixed Number

Proper (8/13)

Decimal Value

0.615385

Percentage

61.5385%

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Step-by-Step Solution: 4/13 + 12/39

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 4/13 by 3, and multiply the numerator and denominator of 12/39 by 1 so both fractions share the common base 39.

4 × 3/13 × 3 = 12/39 and 12 × 1/39 × 1 = 12/39

Step 3

Add the Numerators

Now add the numerators (12 + 12 = 24) and keep the common denominator 39 unchanged.

12 + 12/39 = 24/39

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 24 and 39, which is 3. Divide both the numerator and denominator by 3.

24 ÷ 3/39 ÷ 3 = 8/13

Step 5

Decimal & Percentage Representation

Dividing the numerator 8 by denominator 13 produces a repeating decimal (approximately 0.615385, or 61.5385%).

8 ÷ 13 = 0.615385 (61.5385%)

Visual Representation

The diagram below illustrates 4/13 plus 12/39 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`8/13`
Mixed Number Form	`8/13`
Decimal Form	`0.615385`
Percentage	`61.5385%`

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Frequently Asked Questions

What is 4/13 plus 12/39 as a fraction?

4/13 + 12/39 in simplest fraction form is 8/13.

What is 4/13 plus 12/39 as a decimal?

4/13 + 12/39 converted to a decimal is 0.615385.

What is 4/13 plus 12/39 as a percentage?

4/13 + 12/39 expressed as a percentage is 61.5385%.

Does 4/13 plus 12/39 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.615385...) because the denominator contains prime factors other than 2 and 5.