What is 3/29 plus 9/39? (Answer: 126/377)

Exact Answer

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Problem: What is 3/29 plus 9/39?
Formula / Expression: 3/29 + 9/39
Final Answer: 126/377
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 29 and 39 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 29 × 39 = 1131.
Working: LCD(29, 39) = 1131

Step 2: Convert to Equivalent Fractions with Common Denominator 1131
Multiply the numerator and denominator of 3/29 by 39, and multiply the numerator and denominator of 9/39 by 29 so both fractions share the common base 1131.
Working: 3 × 39/29 × 39 = 117/1131 and 9 × 29/39 × 29 = 261/1131

Step 3: Add the Numerators
Now add the numerators (117 + 261 = 378) and keep the common denominator 1131 unchanged.
Working: 117 + 261/1131 = 378/1131

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 378 and 1131, which is 3. Divide both the numerator and denominator by 3.
Working: 378 ÷ 3/1131 ÷ 3 = 126/377

Step 5: Decimal & Percentage Representation
Dividing the numerator 126 by denominator 377 produces a repeating decimal (approximately 0.334218, or 33.4218%).
Working: 126 ÷ 377 = 0.334218 (33.4218%)

Key Values:
- Simplified Fraction: 126/377
- Mixed Number Form: 126/377
- Decimal Value: 0.334218
- Percentage: 33.4218%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-29-plus-9-39/
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3/29 + 9/39 = 126/377

Simplified Fraction

126/377

Mixed Number

Proper (126/377)

Decimal Value

0.334218

Percentage

33.4218%

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Step-by-Step Solution: 3/29 + 9/39

Step 1

Find the Least Common Denominator (LCD)

The denominators 29 and 39 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 29 × 39 = 1131.

LCD(29, 39) = 1131

Step 2

Convert to Equivalent Fractions with Common Denominator 1131

Multiply the numerator and denominator of 3/29 by 39, and multiply the numerator and denominator of 9/39 by 29 so both fractions share the common base 1131.

3 × 39/29 × 39 = 117/1131 and 9 × 29/39 × 29 = 261/1131

Step 3

Add the Numerators

Now add the numerators (117 + 261 = 378) and keep the common denominator 1131 unchanged.

117 + 261/1131 = 378/1131

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 378 and 1131, which is 3. Divide both the numerator and denominator by 3.

378 ÷ 3/1131 ÷ 3 = 126/377

Step 5

Decimal & Percentage Representation

Dividing the numerator 126 by denominator 377 produces a repeating decimal (approximately 0.334218, or 33.4218%).

126 ÷ 377 = 0.334218 (33.4218%)

Visual Representation

The diagram below illustrates 3/29 plus 9/39 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`126/377`
Mixed Number Form	`126/377`
Decimal Form	`0.334218`
Percentage	`33.4218%`

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Frequently Asked Questions

What is 3/29 plus 9/39 as a fraction?

3/29 + 9/39 in simplest fraction form is 126/377.

What is 3/29 plus 9/39 as a decimal?

3/29 + 9/39 converted to a decimal is 0.334218.

What is 3/29 plus 9/39 as a percentage?

3/29 + 9/39 expressed as a percentage is 33.4218%.

Does 3/29 plus 9/39 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.334218...) because the denominator contains prime factors other than 2 and 5.