What is 3/35 plus 9/13? (Answer: 354/455)

Exact Answer

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Problem: What is 3/35 plus 9/13?
Formula / Expression: 3/35 + 9/13
Final Answer: 354/455
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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 3/35 by 13, and multiply the numerator and denominator of 9/13 by 35 so both fractions share the common base 455.
Working: 3 × 13/35 × 13 = 39/455 and 9 × 35/13 × 35 = 315/455

Step 3: Add the Numerators
Now add the numerators (39 + 315 = 354) and keep the common denominator 455 unchanged.
Working: 39 + 315/455 = 354/455

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 354 and 455 is 1, confirming that 354/455 cannot be reduced further—it is already in its simplest irreducible form.
Working: 354/455

Step 5: Decimal & Percentage Representation
Dividing the numerator 354 by denominator 455 produces a repeating decimal (approximately 0.778022, or 77.8022%).
Working: 354 ÷ 455 = 0.778022 (77.8022%)

Key Values:
- Simplified Fraction: 354/455
- Mixed Number Form: 354/455
- Decimal Value: 0.778022
- Percentage: 77.8022%

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Solved with FractionsCalc:
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3/35 + 9/13 = 354/455

Simplified Fraction

354/455

Mixed Number

Proper (354/455)

Decimal Value

0.778022

Percentage

77.8022%

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Step-by-Step Solution: 3/35 + 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 3/35 by 13, and multiply the numerator and denominator of 9/13 by 35 so both fractions share the common base 455.

3 × 13/35 × 13 = 39/455 and 9 × 35/13 × 35 = 315/455

Step 3

Add the Numerators

Now add the numerators (39 + 315 = 354) and keep the common denominator 455 unchanged.

39 + 315/455 = 354/455

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 354 and 455 is 1, confirming that 354/455 cannot be reduced further—it is already in its simplest irreducible form.

354/455

Step 5

Decimal & Percentage Representation

Dividing the numerator 354 by denominator 455 produces a repeating decimal (approximately 0.778022, or 77.8022%).

354 ÷ 455 = 0.778022 (77.8022%)

Visual Representation

The diagram below illustrates 3/35 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`354/455`
Mixed Number Form	`354/455`
Decimal Form	`0.778022`
Percentage	`77.8022%`

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Frequently Asked Questions

What is 3/35 plus 9/13 as a fraction?

3/35 + 9/13 in simplest fraction form is 354/455.

What is 3/35 plus 9/13 as a decimal?

3/35 + 9/13 converted to a decimal is 0.778022.

What is 3/35 plus 9/13 as a percentage?

3/35 + 9/13 expressed as a percentage is 77.8022%.

Does 3/35 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.778022...) because the denominator contains prime factors other than 2 and 5.