What is 2/5 plus 9/13? (Answer: 71/65)

Exact Answer

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Problem: What is 2/5 plus 9/13?
Formula / Expression: 2/5 + 9/13
Final Answer: 1 6/65 (71/65)
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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 2/5 by 13, and multiply the numerator and denominator of 9/13 by 5 so both fractions share the common base 65.
Working: 2 × 13/5 × 13 = 26/65 and 9 × 5/13 × 5 = 45/65

Step 3: Add the Numerators
Now add the numerators (26 + 45 = 71) and keep the common denominator 65 unchanged.
Working: 26 + 45/65 = 71/65

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 71 and 65 is 1, confirming that 71/65 cannot be reduced further—it is already in its simplest irreducible form.
Working: 71/65

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (71) is greater than the denominator (65), divide 71 by 65: it goes in 1 whole time(s) with a remainder of 6, giving the mixed number 1 6/65.
Working: 71/65 = 1 6/65

Step 6: Decimal & Percentage Representation
Dividing the numerator 71 by denominator 65 produces a repeating decimal (approximately 1.092308, or 109.2308%).
Working: 71 ÷ 65 = 1.092308 (109.2308%)

Key Values:
- Simplified Fraction: 71/65
- Mixed Number Form: 1 6/65
- Decimal Value: 1.092308
- Percentage: 109.2308%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-5-plus-9-13/
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2/5 + 9/13 = 71/65

Simplified Fraction

71/65

Mixed Number

1 6/65

Decimal Value

1.092308

Percentage

109.2308%

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Step-by-Step Solution: 2/5 + 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 2/5 by 13, and multiply the numerator and denominator of 9/13 by 5 so both fractions share the common base 65.

2 × 13/5 × 13 = 26/65 and 9 × 5/13 × 5 = 45/65

Step 3

Add the Numerators

Now add the numerators (26 + 45 = 71) and keep the common denominator 65 unchanged.

26 + 45/65 = 71/65

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 71 and 65 is 1, confirming that 71/65 cannot be reduced further—it is already in its simplest irreducible form.

71/65

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (71) is greater than the denominator (65), divide 71 by 65: it goes in 1 whole time(s) with a remainder of 6, giving the mixed number 1 6/65.

71/65 = 16/65

Step 6

Decimal & Percentage Representation

Dividing the numerator 71 by denominator 65 produces a repeating decimal (approximately 1.092308, or 109.2308%).

71 ÷ 65 = 1.092308 (109.2308%)

Visual Representation

The diagram below illustrates 2/5 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`71/65`
Mixed Number Form	`1 6/65`
Decimal Form	`1.092308`
Percentage	`109.2308%`

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Frequently Asked Questions

What is 2/5 plus 9/13 as a fraction?

2/5 + 9/13 in simplest fraction form is 71/65 (or 1 6/65 as a mixed number).

What is 2/5 plus 9/13 as a decimal?

2/5 + 9/13 converted to a decimal is 1.092308.

What is 2/5 plus 9/13 as a percentage?

2/5 + 9/13 expressed as a percentage is 109.2308%.

How do you write 2/5 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 71/65 can be written as the mixed number 1 6/65.

Does 2/5 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.092308...) because the denominator contains prime factors other than 2 and 5.