What is 12/39 plus 7/13? (Answer: 11/13)

Exact Answer

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Problem: What is 12/39 plus 7/13?
Formula / Expression: 12/39 + 7/13
Final Answer: 11/13
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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 12/39 by 1, and multiply the numerator and denominator of 7/13 by 3 so both fractions share the common base 39.
Working: 12 × 1/39 × 1 = 12/39 and 7 × 3/13 × 3 = 21/39

Step 3: Add the Numerators
Now add the numerators (12 + 21 = 33) and keep the common denominator 39 unchanged.
Working: 12 + 21/39 = 33/39

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 33 and 39, which is 3. Divide both the numerator and denominator by 3.
Working: 33 ÷ 3/39 ÷ 3 = 11/13

Step 5: Decimal & Percentage Representation
Dividing the numerator 11 by denominator 13 produces a repeating decimal (approximately 0.846154, or 84.6154%).
Working: 11 ÷ 13 = 0.846154 (84.6154%)

Key Values:
- Simplified Fraction: 11/13
- Mixed Number Form: 11/13
- Decimal Value: 0.846154
- Percentage: 84.6154%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-12-39-plus-7-13/
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12/39 + 7/13 = 11/13

Simplified Fraction

11/13

Mixed Number

Proper (11/13)

Decimal Value

0.846154

Percentage

84.6154%

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Step-by-Step Solution: 12/39 + 7/13

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 12/39 by 1, and multiply the numerator and denominator of 7/13 by 3 so both fractions share the common base 39.

12 × 1/39 × 1 = 12/39 and 7 × 3/13 × 3 = 21/39

Step 3

Add the Numerators

Now add the numerators (12 + 21 = 33) and keep the common denominator 39 unchanged.

12 + 21/39 = 33/39

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 33 and 39, which is 3. Divide both the numerator and denominator by 3.

33 ÷ 3/39 ÷ 3 = 11/13

Step 5

Decimal & Percentage Representation

Dividing the numerator 11 by denominator 13 produces a repeating decimal (approximately 0.846154, or 84.6154%).

11 ÷ 13 = 0.846154 (84.6154%)

Visual Representation

The diagram below illustrates 12/39 plus 7/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`11/13`
Mixed Number Form	`11/13`
Decimal Form	`0.846154`
Percentage	`84.6154%`

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Frequently Asked Questions

What is 12/39 plus 7/13 as a fraction?

12/39 + 7/13 in simplest fraction form is 11/13.

What is 12/39 plus 7/13 as a decimal?

12/39 + 7/13 converted to a decimal is 0.846154.

What is 12/39 plus 7/13 as a percentage?

12/39 + 7/13 expressed as a percentage is 84.6154%.

Does 12/39 plus 7/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.846154...) because the denominator contains prime factors other than 2 and 5.