What is 3/30 plus 9/39? (Answer: 43/130)

Exact Answer

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Problem: What is 3/30 plus 9/39?
Formula / Expression: 3/30 + 9/39
Final Answer: 43/130
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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 3/30 by 13, and multiply the numerator and denominator of 9/39 by 10 so both fractions share the common base 390.
Working: 3 × 13/30 × 13 = 39/390 and 9 × 10/39 × 10 = 90/390

Step 3: Add the Numerators
Now add the numerators (39 + 90 = 129) and keep the common denominator 390 unchanged.
Working: 39 + 90/390 = 129/390

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 129 and 390, which is 3. Divide both the numerator and denominator by 3.
Working: 129 ÷ 3/390 ÷ 3 = 43/130

Step 5: Decimal & Percentage Representation
Dividing the numerator 43 by denominator 130 produces a repeating decimal (approximately 0.330769, or 33.0769%).
Working: 43 ÷ 130 = 0.330769 (33.0769%)

Key Values:
- Simplified Fraction: 43/130
- Mixed Number Form: 43/130
- Decimal Value: 0.330769
- Percentage: 33.0769%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-30-plus-9-39/
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3/30 + 9/39 = 43/130

Simplified Fraction

43/130

Mixed Number

Proper (43/130)

Decimal Value

0.330769

Percentage

33.0769%

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Step-by-Step Solution: 3/30 + 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 3/30 by 13, and multiply the numerator and denominator of 9/39 by 10 so both fractions share the common base 390.

3 × 13/30 × 13 = 39/390 and 9 × 10/39 × 10 = 90/390

Step 3

Add the Numerators

Now add the numerators (39 + 90 = 129) and keep the common denominator 390 unchanged.

39 + 90/390 = 129/390

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 129 and 390, which is 3. Divide both the numerator and denominator by 3.

129 ÷ 3/390 ÷ 3 = 43/130

Step 5

Decimal & Percentage Representation

Dividing the numerator 43 by denominator 130 produces a repeating decimal (approximately 0.330769, or 33.0769%).

43 ÷ 130 = 0.330769 (33.0769%)

Visual Representation

The diagram below illustrates 3/30 plus 9/39 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`43/130`
Mixed Number Form	`43/130`
Decimal Form	`0.330769`
Percentage	`33.0769%`

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Frequently Asked Questions

What is 3/30 plus 9/39 as a fraction?

3/30 + 9/39 in simplest fraction form is 43/130.

What is 3/30 plus 9/39 as a decimal?

3/30 + 9/39 converted to a decimal is 0.330769.

What is 3/30 plus 9/39 as a percentage?

3/30 + 9/39 expressed as a percentage is 33.0769%.

Does 3/30 plus 9/39 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.330769...) because the denominator contains prime factors other than 2 and 5.