What is 14/30 plus 9/13? (Answer: 226/195)

Exact Answer

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Problem: What is 14/30 plus 9/13?
Formula / Expression: 14/30 + 9/13
Final Answer: 1 31/195 (226/195)
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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 14/30 by 13, and multiply the numerator and denominator of 9/13 by 30 so both fractions share the common base 390.
Working: 14 × 13/30 × 13 = 182/390 and 9 × 30/13 × 30 = 270/390

Step 3: Add the Numerators
Now add the numerators (182 + 270 = 452) and keep the common denominator 390 unchanged.
Working: 182 + 270/390 = 452/390

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 452 and 390, which is 2. Divide both the numerator and denominator by 2.
Working: 452 ÷ 2/390 ÷ 2 = 226/195

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (226) is greater than the denominator (195), divide 226 by 195: it goes in 1 whole time(s) with a remainder of 31, giving the mixed number 1 31/195.
Working: 226/195 = 1 31/195

Step 6: Decimal & Percentage Representation
Dividing the numerator 226 by denominator 195 produces a repeating decimal (approximately 1.158974, or 115.8974%).
Working: 226 ÷ 195 = 1.158974 (115.8974%)

Key Values:
- Simplified Fraction: 226/195
- Mixed Number Form: 1 31/195
- Decimal Value: 1.158974
- Percentage: 115.8974%

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14/30 + 9/13 = 226/195

Simplified Fraction

226/195

Mixed Number

1 31/195

Decimal Value

1.158974

Percentage

115.8974%

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Step-by-Step Solution: 14/30 + 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 14/30 by 13, and multiply the numerator and denominator of 9/13 by 30 so both fractions share the common base 390.

14 × 13/30 × 13 = 182/390 and 9 × 30/13 × 30 = 270/390

Step 3

Add the Numerators

Now add the numerators (182 + 270 = 452) and keep the common denominator 390 unchanged.

182 + 270/390 = 452/390

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 452 and 390, which is 2. Divide both the numerator and denominator by 2.

452 ÷ 2/390 ÷ 2 = 226/195

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (226) is greater than the denominator (195), divide 226 by 195: it goes in 1 whole time(s) with a remainder of 31, giving the mixed number 1 31/195.

226/195 = 131/195

Step 6

Decimal & Percentage Representation

Dividing the numerator 226 by denominator 195 produces a repeating decimal (approximately 1.158974, or 115.8974%).

226 ÷ 195 = 1.158974 (115.8974%)

Visual Representation

The diagram below illustrates 14/30 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`226/195`
Mixed Number Form	`1 31/195`
Decimal Form	`1.158974`
Percentage	`115.8974%`

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Frequently Asked Questions

What is 14/30 plus 9/13 as a fraction?

14/30 + 9/13 in simplest fraction form is 226/195 (or 1 31/195 as a mixed number).

What is 14/30 plus 9/13 as a decimal?

14/30 + 9/13 converted to a decimal is 1.158974.

What is 14/30 plus 9/13 as a percentage?

14/30 + 9/13 expressed as a percentage is 115.8974%.

How do you write 14/30 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 226/195 can be written as the mixed number 1 31/195.

Does 14/30 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.158974...) because the denominator contains prime factors other than 2 and 5.