What is 18/35 plus 9/13? (Answer: 549/455)

Exact Answer

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Problem: What is 18/35 plus 9/13?
Formula / Expression: 18/35 + 9/13
Final Answer: 1 94/455 (549/455)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 35 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 35 × 13 = 455.
Working: LCD(35, 13) = 455

Step 2: Convert to Equivalent Fractions with Common Denominator 455
Multiply the numerator and denominator of 18/35 by 13, and multiply the numerator and denominator of 9/13 by 35 so both fractions share the common base 455.
Working: 18 × 13/35 × 13 = 234/455 and 9 × 35/13 × 35 = 315/455

Step 3: Add the Numerators
Now add the numerators (234 + 315 = 549) and keep the common denominator 455 unchanged.
Working: 234 + 315/455 = 549/455

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 549 and 455 is 1, confirming that 549/455 cannot be reduced further—it is already in its simplest irreducible form.
Working: 549/455

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (549) is greater than the denominator (455), divide 549 by 455: it goes in 1 whole time(s) with a remainder of 94, giving the mixed number 1 94/455.
Working: 549/455 = 1 94/455

Step 6: Decimal & Percentage Representation
Dividing the numerator 549 by denominator 455 produces a repeating decimal (approximately 1.206593, or 120.6593%).
Working: 549 ÷ 455 = 1.206593 (120.6593%)

Key Values:
- Simplified Fraction: 549/455
- Mixed Number Form: 1 94/455
- Decimal Value: 1.206593
- Percentage: 120.6593%

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Solved with FractionsCalc:
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18/35 + 9/13 = 549/455

Simplified Fraction

549/455

Mixed Number

1 94/455

Decimal Value

1.206593

Percentage

120.6593%

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Step-by-Step Solution: 18/35 + 9/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 35 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 35 × 13 = 455.

LCD(35, 13) = 455

Step 2

Convert to Equivalent Fractions with Common Denominator 455

Multiply the numerator and denominator of 18/35 by 13, and multiply the numerator and denominator of 9/13 by 35 so both fractions share the common base 455.

18 × 13/35 × 13 = 234/455 and 9 × 35/13 × 35 = 315/455

Step 3

Add the Numerators

Now add the numerators (234 + 315 = 549) and keep the common denominator 455 unchanged.

234 + 315/455 = 549/455

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 549 and 455 is 1, confirming that 549/455 cannot be reduced further—it is already in its simplest irreducible form.

549/455

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (549) is greater than the denominator (455), divide 549 by 455: it goes in 1 whole time(s) with a remainder of 94, giving the mixed number 1 94/455.

549/455 = 194/455

Step 6

Decimal & Percentage Representation

Dividing the numerator 549 by denominator 455 produces a repeating decimal (approximately 1.206593, or 120.6593%).

549 ÷ 455 = 1.206593 (120.6593%)

Visual Representation

The diagram below illustrates 18/35 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`549/455`
Mixed Number Form	`1 94/455`
Decimal Form	`1.206593`
Percentage	`120.6593%`

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Frequently Asked Questions

What is 18/35 plus 9/13 as a fraction?

18/35 + 9/13 in simplest fraction form is 549/455 (or 1 94/455 as a mixed number).

What is 18/35 plus 9/13 as a decimal?

18/35 + 9/13 converted to a decimal is 1.206593.

What is 18/35 plus 9/13 as a percentage?

18/35 + 9/13 expressed as a percentage is 120.6593%.

How do you write 18/35 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 549/455 can be written as the mixed number 1 94/455.

Does 18/35 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.206593...) because the denominator contains prime factors other than 2 and 5.