What is 3/5 plus 9/13? (Answer: 84/65)

Exact Answer

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Problem: What is 3/5 plus 9/13?
Formula / Expression: 3/5 + 9/13
Final Answer: 1 19/65 (84/65)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 5 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 13 = 65.
Working: LCD(5, 13) = 65

Step 2: Convert to Equivalent Fractions with Common Denominator 65
Multiply the numerator and denominator of 3/5 by 13, and multiply the numerator and denominator of 9/13 by 5 so both fractions share the common base 65.
Working: 3 × 13/5 × 13 = 39/65 and 9 × 5/13 × 5 = 45/65

Step 3: Add the Numerators
Now add the numerators (39 + 45 = 84) and keep the common denominator 65 unchanged.
Working: 39 + 45/65 = 84/65

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 84 and 65 is 1, confirming that 84/65 cannot be reduced further—it is already in its simplest irreducible form.
Working: 84/65

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (84) is greater than the denominator (65), divide 84 by 65: it goes in 1 whole time(s) with a remainder of 19, giving the mixed number 1 19/65.
Working: 84/65 = 1 19/65

Step 6: Decimal & Percentage Representation
Dividing the numerator 84 by denominator 65 produces a repeating decimal (approximately 1.292308, or 129.2308%).
Working: 84 ÷ 65 = 1.292308 (129.2308%)

Key Values:
- Simplified Fraction: 84/65
- Mixed Number Form: 1 19/65
- Decimal Value: 1.292308
- Percentage: 129.2308%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-5-plus-9-13/
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3/5 + 9/13 = 84/65

Simplified Fraction

84/65

Mixed Number

1 19/65

Decimal Value

1.292308

Percentage

129.2308%

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Step-by-Step Solution: 3/5 + 9/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 5 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 13 = 65.

LCD(5, 13) = 65

Step 2

Convert to Equivalent Fractions with Common Denominator 65

Multiply the numerator and denominator of 3/5 by 13, and multiply the numerator and denominator of 9/13 by 5 so both fractions share the common base 65.

3 × 13/5 × 13 = 39/65 and 9 × 5/13 × 5 = 45/65

Step 3

Add the Numerators

Now add the numerators (39 + 45 = 84) and keep the common denominator 65 unchanged.

39 + 45/65 = 84/65

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 84 and 65 is 1, confirming that 84/65 cannot be reduced further—it is already in its simplest irreducible form.

84/65

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (84) is greater than the denominator (65), divide 84 by 65: it goes in 1 whole time(s) with a remainder of 19, giving the mixed number 1 19/65.

84/65 = 119/65

Step 6

Decimal & Percentage Representation

Dividing the numerator 84 by denominator 65 produces a repeating decimal (approximately 1.292308, or 129.2308%).

84 ÷ 65 = 1.292308 (129.2308%)

Visual Representation

The diagram below illustrates 3/5 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`84/65`
Mixed Number Form	`1 19/65`
Decimal Form	`1.292308`
Percentage	`129.2308%`

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Frequently Asked Questions

What is 3/5 plus 9/13 as a fraction?

3/5 + 9/13 in simplest fraction form is 84/65 (or 1 19/65 as a mixed number).

What is 3/5 plus 9/13 as a decimal?

3/5 + 9/13 converted to a decimal is 1.292308.

What is 3/5 plus 9/13 as a percentage?

3/5 + 9/13 expressed as a percentage is 129.2308%.

How do you write 3/5 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 84/65 can be written as the mixed number 1 19/65.

Does 3/5 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.292308...) because the denominator contains prime factors other than 2 and 5.