What is 2/5 plus 7/13? (Answer: 61/65)

Exact Answer

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Problem: What is 2/5 plus 7/13?
Formula / Expression: 2/5 + 7/13
Final Answer: 61/65
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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 7/13 by 5 so both fractions share the common base 65.
Working: 2 × 13/5 × 13 = 26/65 and 7 × 5/13 × 5 = 35/65

Step 3: Add the Numerators
Now add the numerators (26 + 35 = 61) and keep the common denominator 65 unchanged.
Working: 26 + 35/65 = 61/65

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 61 and 65 is 1, confirming that 61/65 cannot be reduced further—it is already in its simplest irreducible form.
Working: 61/65

Step 5: Decimal & Percentage Representation
Dividing the numerator 61 by denominator 65 produces a repeating decimal (approximately 0.938462, or 93.8462%).
Working: 61 ÷ 65 = 0.938462 (93.8462%)

Key Values:
- Simplified Fraction: 61/65
- Mixed Number Form: 61/65
- Decimal Value: 0.938462
- Percentage: 93.8462%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-5-plus-7-13/
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2/5 + 7/13 = 61/65

Simplified Fraction

61/65

Mixed Number

Proper (61/65)

Decimal Value

0.938462

Percentage

93.8462%

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Step-by-Step Solution: 2/5 + 7/13

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 7/13 by 5 so both fractions share the common base 65.

2 × 13/5 × 13 = 26/65 and 7 × 5/13 × 5 = 35/65

Step 3

Add the Numerators

Now add the numerators (26 + 35 = 61) and keep the common denominator 65 unchanged.

26 + 35/65 = 61/65

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 61 and 65 is 1, confirming that 61/65 cannot be reduced further—it is already in its simplest irreducible form.

61/65

Step 5

Decimal & Percentage Representation

Dividing the numerator 61 by denominator 65 produces a repeating decimal (approximately 0.938462, or 93.8462%).

61 ÷ 65 = 0.938462 (93.8462%)

Visual Representation

The diagram below illustrates 2/5 plus 7/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`61/65`
Mixed Number Form	`61/65`
Decimal Form	`0.938462`
Percentage	`93.8462%`

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Frequently Asked Questions

What is 2/5 plus 7/13 as a fraction?

2/5 + 7/13 in simplest fraction form is 61/65.

What is 2/5 plus 7/13 as a decimal?

2/5 + 7/13 converted to a decimal is 0.938462.

What is 2/5 plus 7/13 as a percentage?

2/5 + 7/13 expressed as a percentage is 93.8462%.

Does 2/5 plus 7/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.938462...) because the denominator contains prime factors other than 2 and 5.