What is 9/39 plus 3/12? (Answer: 25/52)

Exact Answer

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Problem: What is 9/39 plus 3/12?
Formula / Expression: 9/39 + 3/12
Final Answer: 25/52
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 39 and 12 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 156 (which is smaller than their product 39 × 12 = 468, keeping the calculation simpler).
Working: LCD(39, 12) = 156

Step 2: Convert to Equivalent Fractions with Common Denominator 156
Multiply the numerator and denominator of 9/39 by 4, and multiply the numerator and denominator of 3/12 by 13 so both fractions share the common base 156.
Working: 9 × 4/39 × 4 = 36/156 and 3 × 13/12 × 13 = 39/156

Step 3: Add the Numerators
Now add the numerators (36 + 39 = 75) and keep the common denominator 156 unchanged.
Working: 36 + 39/156 = 75/156

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 75 and 156, which is 3. Divide both the numerator and denominator by 3.
Working: 75 ÷ 3/156 ÷ 3 = 25/52

Step 5: Decimal & Percentage Representation
Dividing the numerator 25 by denominator 52 produces a repeating decimal (approximately 0.480769, or 48.0769%).
Working: 25 ÷ 52 = 0.480769 (48.0769%)

Key Values:
- Simplified Fraction: 25/52
- Mixed Number Form: 25/52
- Decimal Value: 0.480769
- Percentage: 48.0769%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-9-39-plus-3-12/
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9/39 + 3/12 = 25/52

Simplified Fraction

25/52

Mixed Number

Proper (25/52)

Decimal Value

0.480769

Percentage

48.0769%

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Step-by-Step Solution: 9/39 + 3/12

Step 1

Find the Least Common Denominator (LCD)

The denominators 39 and 12 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 156 (which is smaller than their product 39 × 12 = 468, keeping the calculation simpler).

LCD(39, 12) = 156

Step 2

Convert to Equivalent Fractions with Common Denominator 156

Multiply the numerator and denominator of 9/39 by 4, and multiply the numerator and denominator of 3/12 by 13 so both fractions share the common base 156.

9 × 4/39 × 4 = 36/156 and 3 × 13/12 × 13 = 39/156

Step 3

Add the Numerators

Now add the numerators (36 + 39 = 75) and keep the common denominator 156 unchanged.

36 + 39/156 = 75/156

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 75 and 156, which is 3. Divide both the numerator and denominator by 3.

75 ÷ 3/156 ÷ 3 = 25/52

Step 5

Decimal & Percentage Representation

Dividing the numerator 25 by denominator 52 produces a repeating decimal (approximately 0.480769, or 48.0769%).

25 ÷ 52 = 0.480769 (48.0769%)

Visual Representation

The diagram below illustrates 9/39 plus 3/12 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`25/52`
Mixed Number Form	`25/52`
Decimal Form	`0.480769`
Percentage	`48.0769%`

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Frequently Asked Questions

What is 9/39 plus 3/12 as a fraction?

9/39 + 3/12 in simplest fraction form is 25/52.

What is 9/39 plus 3/12 as a decimal?

9/39 + 3/12 converted to a decimal is 0.480769.

What is 9/39 plus 3/12 as a percentage?

9/39 + 3/12 expressed as a percentage is 48.0769%.

Does 9/39 plus 3/12 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.480769...) because the denominator contains prime factors other than 2 and 5.