What is 13/30 plus 7/13? (Answer: 379/390)

Exact Answer

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Problem: What is 13/30 plus 7/13?
Formula / Expression: 13/30 + 7/13
Final Answer: 379/390
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 390
Multiply the numerator and denominator of 13/30 by 13, and multiply the numerator and denominator of 7/13 by 30 so both fractions share the common base 390.
Working: 13 × 13/30 × 13 = 169/390 and 7 × 30/13 × 30 = 210/390

Step 3: Add the Numerators
Now add the numerators (169 + 210 = 379) and keep the common denominator 390 unchanged.
Working: 169 + 210/390 = 379/390

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 379 and 390 is 1, confirming that 379/390 cannot be reduced further—it is already in its simplest irreducible form.
Working: 379/390

Step 5: Decimal & Percentage Representation
Dividing the numerator 379 by denominator 390 produces a repeating decimal (approximately 0.971795, or 97.1795%).
Working: 379 ÷ 390 = 0.971795 (97.1795%)

Key Values:
- Simplified Fraction: 379/390
- Mixed Number Form: 379/390
- Decimal Value: 0.971795
- Percentage: 97.1795%

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Solved with FractionsCalc:
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13/30 + 7/13 = 379/390

Simplified Fraction

379/390

Mixed Number

Proper (379/390)

Decimal Value

0.971795

Percentage

97.1795%

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

Step 1

Find the Least Common Denominator (LCD)

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

LCD(30, 13) = 390

Step 2

Convert to Equivalent Fractions with Common Denominator 390

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

13 × 13/30 × 13 = 169/390 and 7 × 30/13 × 30 = 210/390

Step 3

Add the Numerators

Now add the numerators (169 + 210 = 379) and keep the common denominator 390 unchanged.

169 + 210/390 = 379/390

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 379 and 390 is 1, confirming that 379/390 cannot be reduced further—it is already in its simplest irreducible form.

379/390

Step 5

Decimal & Percentage Representation

Dividing the numerator 379 by denominator 390 produces a repeating decimal (approximately 0.971795, or 97.1795%).

379 ÷ 390 = 0.971795 (97.1795%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`379/390`
Mixed Number Form	`379/390`
Decimal Form	`0.971795`
Percentage	`97.1795%`

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Frequently Asked Questions

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

13/30 + 7/13 in simplest fraction form is 379/390.

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

13/30 + 7/13 converted to a decimal is 0.971795.

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

13/30 + 7/13 expressed as a percentage is 97.1795%.

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

It results in a repeating decimal (approximately 0.971795...) because the denominator contains prime factors other than 2 and 5.