What is 17/33 plus 9/13? (Answer: 518/429)

Exact Answer

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Problem: What is 17/33 plus 9/13?
Formula / Expression: 17/33 + 9/13
Final Answer: 1 89/429 (518/429)
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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 17/33 by 13, and multiply the numerator and denominator of 9/13 by 33 so both fractions share the common base 429.
Working: 17 × 13/33 × 13 = 221/429 and 9 × 33/13 × 33 = 297/429

Step 3: Add the Numerators
Now add the numerators (221 + 297 = 518) and keep the common denominator 429 unchanged.
Working: 221 + 297/429 = 518/429

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 518 and 429 is 1, confirming that 518/429 cannot be reduced further—it is already in its simplest irreducible form.
Working: 518/429

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (518) is greater than the denominator (429), divide 518 by 429: it goes in 1 whole time(s) with a remainder of 89, giving the mixed number 1 89/429.
Working: 518/429 = 1 89/429

Step 6: Decimal & Percentage Representation
Dividing the numerator 518 by denominator 429 produces a repeating decimal (approximately 1.207459, or 120.7459%).
Working: 518 ÷ 429 = 1.207459 (120.7459%)

Key Values:
- Simplified Fraction: 518/429
- Mixed Number Form: 1 89/429
- Decimal Value: 1.207459
- Percentage: 120.7459%

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Solved with FractionsCalc:
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17/33 + 9/13 = 518/429

Simplified Fraction

518/429

Mixed Number

1 89/429

Decimal Value

1.207459

Percentage

120.7459%

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Step-by-Step Solution: 17/33 + 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 17/33 by 13, and multiply the numerator and denominator of 9/13 by 33 so both fractions share the common base 429.

17 × 13/33 × 13 = 221/429 and 9 × 33/13 × 33 = 297/429

Step 3

Add the Numerators

Now add the numerators (221 + 297 = 518) and keep the common denominator 429 unchanged.

221 + 297/429 = 518/429

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 518 and 429 is 1, confirming that 518/429 cannot be reduced further—it is already in its simplest irreducible form.

518/429

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (518) is greater than the denominator (429), divide 518 by 429: it goes in 1 whole time(s) with a remainder of 89, giving the mixed number 1 89/429.

518/429 = 189/429

Step 6

Decimal & Percentage Representation

Dividing the numerator 518 by denominator 429 produces a repeating decimal (approximately 1.207459, or 120.7459%).

518 ÷ 429 = 1.207459 (120.7459%)

Visual Representation

The diagram below illustrates 17/33 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`518/429`
Mixed Number Form	`1 89/429`
Decimal Form	`1.207459`
Percentage	`120.7459%`

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Frequently Asked Questions

What is 17/33 plus 9/13 as a fraction?

17/33 + 9/13 in simplest fraction form is 518/429 (or 1 89/429 as a mixed number).

What is 17/33 plus 9/13 as a decimal?

17/33 + 9/13 converted to a decimal is 1.207459.

What is 17/33 plus 9/13 as a percentage?

17/33 + 9/13 expressed as a percentage is 120.7459%.

How do you write 17/33 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 518/429 can be written as the mixed number 1 89/429.

Does 17/33 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.207459...) because the denominator contains prime factors other than 2 and 5.