What is 2/30 plus 9/39? (Answer: 58/195)

Exact Answer

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Problem: What is 2/30 plus 9/39?
Formula / Expression: 2/30 + 9/39
Final Answer: 58/195
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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 9/39 by 10 so both fractions share the common base 390.
Working: 2 × 13/30 × 13 = 26/390 and 9 × 10/39 × 10 = 90/390

Step 3: Add the Numerators
Now add the numerators (26 + 90 = 116) and keep the common denominator 390 unchanged.
Working: 26 + 90/390 = 116/390

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 116 and 390, which is 2. Divide both the numerator and denominator by 2.
Working: 116 ÷ 2/390 ÷ 2 = 58/195

Step 5: Decimal & Percentage Representation
Dividing the numerator 58 by denominator 195 produces a repeating decimal (approximately 0.297436, or 29.7436%).
Working: 58 ÷ 195 = 0.297436 (29.7436%)

Key Values:
- Simplified Fraction: 58/195
- Mixed Number Form: 58/195
- Decimal Value: 0.297436
- Percentage: 29.7436%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-30-plus-9-39/
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2/30 + 9/39 = 58/195

Simplified Fraction

58/195

Mixed Number

Proper (58/195)

Decimal Value

0.297436

Percentage

29.7436%

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Step-by-Step Solution: 2/30 + 9/39

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 9/39 by 10 so both fractions share the common base 390.

2 × 13/30 × 13 = 26/390 and 9 × 10/39 × 10 = 90/390

Step 3

Add the Numerators

Now add the numerators (26 + 90 = 116) and keep the common denominator 390 unchanged.

26 + 90/390 = 116/390

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 116 and 390, which is 2. Divide both the numerator and denominator by 2.

116 ÷ 2/390 ÷ 2 = 58/195

Step 5

Decimal & Percentage Representation

Dividing the numerator 58 by denominator 195 produces a repeating decimal (approximately 0.297436, or 29.7436%).

58 ÷ 195 = 0.297436 (29.7436%)

Visual Representation

The diagram below illustrates 2/30 plus 9/39 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`58/195`
Mixed Number Form	`58/195`
Decimal Form	`0.297436`
Percentage	`29.7436%`

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Frequently Asked Questions

What is 2/30 plus 9/39 as a fraction?

2/30 + 9/39 in simplest fraction form is 58/195.

What is 2/30 plus 9/39 as a decimal?

2/30 + 9/39 converted to a decimal is 0.297436.

What is 2/30 plus 9/39 as a percentage?

2/30 + 9/39 expressed as a percentage is 29.7436%.

Does 2/30 plus 9/39 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.297436...) because the denominator contains prime factors other than 2 and 5.