What is 3/13 plus 7/30? (Answer: 181/390)

Exact Answer

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Problem: What is 3/13 plus 7/30?
Formula / Expression: 3/13 + 7/30
Final Answer: 181/390
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 13 and 30 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 30 = 390.
Working: LCD(13, 30) = 390

Step 2: Convert to Equivalent Fractions with Common Denominator 390
Multiply the numerator and denominator of 3/13 by 30, and multiply the numerator and denominator of 7/30 by 13 so both fractions share the common base 390.
Working: 3 × 30/13 × 30 = 90/390 and 7 × 13/30 × 13 = 91/390

Step 3: Add the Numerators
Now add the numerators (90 + 91 = 181) and keep the common denominator 390 unchanged.
Working: 90 + 91/390 = 181/390

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 181 and 390 is 1, confirming that 181/390 cannot be reduced further—it is already in its simplest irreducible form.
Working: 181/390

Step 5: Decimal & Percentage Representation
Dividing the numerator 181 by denominator 390 produces a repeating decimal (approximately 0.464103, or 46.4103%).
Working: 181 ÷ 390 = 0.464103 (46.4103%)

Key Values:
- Simplified Fraction: 181/390
- Mixed Number Form: 181/390
- Decimal Value: 0.464103
- Percentage: 46.4103%

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Solved with FractionsCalc:
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3/13 + 7/30 = 181/390

Simplified Fraction

181/390

Mixed Number

Proper (181/390)

Decimal Value

0.464103

Percentage

46.4103%

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Step-by-Step Solution: 3/13 + 7/30

Step 1

Find the Least Common Denominator (LCD)

The denominators 13 and 30 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 30 = 390.

LCD(13, 30) = 390

Step 2

Convert to Equivalent Fractions with Common Denominator 390

Multiply the numerator and denominator of 3/13 by 30, and multiply the numerator and denominator of 7/30 by 13 so both fractions share the common base 390.

3 × 30/13 × 30 = 90/390 and 7 × 13/30 × 13 = 91/390

Step 3

Add the Numerators

Now add the numerators (90 + 91 = 181) and keep the common denominator 390 unchanged.

90 + 91/390 = 181/390

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 181 and 390 is 1, confirming that 181/390 cannot be reduced further—it is already in its simplest irreducible form.

181/390

Step 5

Decimal & Percentage Representation

Dividing the numerator 181 by denominator 390 produces a repeating decimal (approximately 0.464103, or 46.4103%).

181 ÷ 390 = 0.464103 (46.4103%)

Visual Representation

The diagram below illustrates 3/13 plus 7/30 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`181/390`
Mixed Number Form	`181/390`
Decimal Form	`0.464103`
Percentage	`46.4103%`

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Frequently Asked Questions

What is 3/13 plus 7/30 as a fraction?

3/13 + 7/30 in simplest fraction form is 181/390.

What is 3/13 plus 7/30 as a decimal?

3/13 + 7/30 converted to a decimal is 0.464103.

What is 3/13 plus 7/30 as a percentage?

3/13 + 7/30 expressed as a percentage is 46.4103%.

Does 3/13 plus 7/30 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.464103...) because the denominator contains prime factors other than 2 and 5.