What is 2/30 plus 4/39? (Answer: 11/65)

Exact Answer

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Problem: What is 2/30 plus 4/39?
Formula / Expression: 2/30 + 4/39
Final Answer: 11/65
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 30 and 39 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 390 (which is smaller than their product 30 × 39 = 1170, keeping the calculation simpler).
Working: LCD(30, 39) = 390

Step 2: Convert to Equivalent Fractions with Common Denominator 390
Multiply the numerator and denominator of 2/30 by 13, and multiply the numerator and denominator of 4/39 by 10 so both fractions share the common base 390.
Working: 2 × 13/30 × 13 = 26/390 and 4 × 10/39 × 10 = 40/390

Step 3: Add the Numerators
Now add the numerators (26 + 40 = 66) and keep the common denominator 390 unchanged.
Working: 26 + 40/390 = 66/390

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 66 and 390, which is 6. Divide both the numerator and denominator by 6.
Working: 66 ÷ 6/390 ÷ 6 = 11/65

Step 5: Decimal & Percentage Representation
Dividing the numerator 11 by denominator 65 produces a repeating decimal (approximately 0.169231, or 16.9231%).
Working: 11 ÷ 65 = 0.169231 (16.9231%)

Key Values:
- Simplified Fraction: 11/65
- Mixed Number Form: 11/65
- Decimal Value: 0.169231
- Percentage: 16.9231%

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Solved with FractionsCalc:
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2/30 + 4/39 = 11/65

Simplified Fraction

11/65

Mixed Number

Proper (11/65)

Decimal Value

0.169231

Percentage

16.9231%

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Step-by-Step Solution: 2/30 + 4/39

Step 1

Find the Least Common Denominator (LCD)

The denominators 30 and 39 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 390 (which is smaller than their product 30 × 39 = 1170, keeping the calculation simpler).

LCD(30, 39) = 390

Step 2

Convert to Equivalent Fractions with Common Denominator 390

Multiply the numerator and denominator of 2/30 by 13, and multiply the numerator and denominator of 4/39 by 10 so both fractions share the common base 390.

2 × 13/30 × 13 = 26/390 and 4 × 10/39 × 10 = 40/390

Step 3

Add the Numerators

Now add the numerators (26 + 40 = 66) and keep the common denominator 390 unchanged.

26 + 40/390 = 66/390

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 66 and 390, which is 6. Divide both the numerator and denominator by 6.

66 ÷ 6/390 ÷ 6 = 11/65

Step 5

Decimal & Percentage Representation

Dividing the numerator 11 by denominator 65 produces a repeating decimal (approximately 0.169231, or 16.9231%).

11 ÷ 65 = 0.169231 (16.9231%)

Visual Representation

The diagram below illustrates 2/30 plus 4/39 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`11/65`
Mixed Number Form	`11/65`
Decimal Form	`0.169231`
Percentage	`16.9231%`

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Frequently Asked Questions

What is 2/30 plus 4/39 as a fraction?

2/30 + 4/39 in simplest fraction form is 11/65.

What is 2/30 plus 4/39 as a decimal?

2/30 + 4/39 converted to a decimal is 0.169231.

What is 2/30 plus 4/39 as a percentage?

2/30 + 4/39 expressed as a percentage is 16.9231%.

Does 2/30 plus 4/39 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.169231...) because the denominator contains prime factors other than 2 and 5.