What is 13/33 plus 9/13? (Answer: 466/429)

Exact Answer

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Problem: What is 13/33 plus 9/13?
Formula / Expression: 13/33 + 9/13
Final Answer: 1 37/429 (466/429)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 33 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 33 × 13 = 429.
Working: LCD(33, 13) = 429

Step 2: Convert to Equivalent Fractions with Common Denominator 429
Multiply the numerator and denominator of 13/33 by 13, and multiply the numerator and denominator of 9/13 by 33 so both fractions share the common base 429.
Working: 13 × 13/33 × 13 = 169/429 and 9 × 33/13 × 33 = 297/429

Step 3: Add the Numerators
Now add the numerators (169 + 297 = 466) and keep the common denominator 429 unchanged.
Working: 169 + 297/429 = 466/429

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 466 and 429 is 1, confirming that 466/429 cannot be reduced further—it is already in its simplest irreducible form.
Working: 466/429

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (466) is greater than the denominator (429), divide 466 by 429: it goes in 1 whole time(s) with a remainder of 37, giving the mixed number 1 37/429.
Working: 466/429 = 1 37/429

Step 6: Decimal & Percentage Representation
Dividing the numerator 466 by denominator 429 produces a repeating decimal (approximately 1.086247, or 108.6247%).
Working: 466 ÷ 429 = 1.086247 (108.6247%)

Key Values:
- Simplified Fraction: 466/429
- Mixed Number Form: 1 37/429
- Decimal Value: 1.086247
- Percentage: 108.6247%

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Solved with FractionsCalc:
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13/33 + 9/13 = 466/429

Simplified Fraction

466/429

Mixed Number

1 37/429

Decimal Value

1.086247

Percentage

108.6247%

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Step-by-Step Solution: 13/33 + 9/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 33 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 33 × 13 = 429.

LCD(33, 13) = 429

Step 2

Convert to Equivalent Fractions with Common Denominator 429

Multiply the numerator and denominator of 13/33 by 13, and multiply the numerator and denominator of 9/13 by 33 so both fractions share the common base 429.

13 × 13/33 × 13 = 169/429 and 9 × 33/13 × 33 = 297/429

Step 3

Add the Numerators

Now add the numerators (169 + 297 = 466) and keep the common denominator 429 unchanged.

169 + 297/429 = 466/429

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 466 and 429 is 1, confirming that 466/429 cannot be reduced further—it is already in its simplest irreducible form.

466/429

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (466) is greater than the denominator (429), divide 466 by 429: it goes in 1 whole time(s) with a remainder of 37, giving the mixed number 1 37/429.

466/429 = 137/429

Step 6

Decimal & Percentage Representation

Dividing the numerator 466 by denominator 429 produces a repeating decimal (approximately 1.086247, or 108.6247%).

466 ÷ 429 = 1.086247 (108.6247%)

Visual Representation

The diagram below illustrates 13/33 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`466/429`
Mixed Number Form	`1 37/429`
Decimal Form	`1.086247`
Percentage	`108.6247%`

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Frequently Asked Questions

What is 13/33 plus 9/13 as a fraction?

13/33 + 9/13 in simplest fraction form is 466/429 (or 1 37/429 as a mixed number).

What is 13/33 plus 9/13 as a decimal?

13/33 + 9/13 converted to a decimal is 1.086247.

What is 13/33 plus 9/13 as a percentage?

13/33 + 9/13 expressed as a percentage is 108.6247%.

How do you write 13/33 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 466/429 can be written as the mixed number 1 37/429.

Does 13/33 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.086247...) because the denominator contains prime factors other than 2 and 5.