What is 11/30 plus 9/13? (Answer: 413/390)

Exact Answer

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Problem: What is 11/30 plus 9/13?
Formula / Expression: 11/30 + 9/13
Final Answer: 1 23/390 (413/390)
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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 11/30 by 13, and multiply the numerator and denominator of 9/13 by 30 so both fractions share the common base 390.
Working: 11 × 13/30 × 13 = 143/390 and 9 × 30/13 × 30 = 270/390

Step 3: Add the Numerators
Now add the numerators (143 + 270 = 413) and keep the common denominator 390 unchanged.
Working: 143 + 270/390 = 413/390

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 413 and 390 is 1, confirming that 413/390 cannot be reduced further—it is already in its simplest irreducible form.
Working: 413/390

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (413) is greater than the denominator (390), divide 413 by 390: it goes in 1 whole time(s) with a remainder of 23, giving the mixed number 1 23/390.
Working: 413/390 = 1 23/390

Step 6: Decimal & Percentage Representation
Dividing the numerator 413 by denominator 390 produces a repeating decimal (approximately 1.058974, or 105.8974%).
Working: 413 ÷ 390 = 1.058974 (105.8974%)

Key Values:
- Simplified Fraction: 413/390
- Mixed Number Form: 1 23/390
- Decimal Value: 1.058974
- Percentage: 105.8974%

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11/30 + 9/13 = 413/390

Simplified Fraction

413/390

Mixed Number

1 23/390

Decimal Value

1.058974

Percentage

105.8974%

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Step-by-Step Solution: 11/30 + 9/13

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 11/30 by 13, and multiply the numerator and denominator of 9/13 by 30 so both fractions share the common base 390.

11 × 13/30 × 13 = 143/390 and 9 × 30/13 × 30 = 270/390

Step 3

Add the Numerators

Now add the numerators (143 + 270 = 413) and keep the common denominator 390 unchanged.

143 + 270/390 = 413/390

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 413 and 390 is 1, confirming that 413/390 cannot be reduced further—it is already in its simplest irreducible form.

413/390

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (413) is greater than the denominator (390), divide 413 by 390: it goes in 1 whole time(s) with a remainder of 23, giving the mixed number 1 23/390.

413/390 = 123/390

Step 6

Decimal & Percentage Representation

Dividing the numerator 413 by denominator 390 produces a repeating decimal (approximately 1.058974, or 105.8974%).

413 ÷ 390 = 1.058974 (105.8974%)

Visual Representation

The diagram below illustrates 11/30 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`413/390`
Mixed Number Form	`1 23/390`
Decimal Form	`1.058974`
Percentage	`105.8974%`

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Frequently Asked Questions

What is 11/30 plus 9/13 as a fraction?

11/30 + 9/13 in simplest fraction form is 413/390 (or 1 23/390 as a mixed number).

What is 11/30 plus 9/13 as a decimal?

11/30 + 9/13 converted to a decimal is 1.058974.

What is 11/30 plus 9/13 as a percentage?

11/30 + 9/13 expressed as a percentage is 105.8974%.

How do you write 11/30 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 413/390 can be written as the mixed number 1 23/390.

Does 11/30 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.058974...) because the denominator contains prime factors other than 2 and 5.