What is 4/13 plus 2/5? (Answer: 46/65)

Exact Answer

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Problem: What is 4/13 plus 2/5?
Formula / Expression: 4/13 + 2/5
Final Answer: 46/65
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 65
Multiply the numerator and denominator of 4/13 by 5, and multiply the numerator and denominator of 2/5 by 13 so both fractions share the common base 65.
Working: 4 × 5/13 × 5 = 20/65 and 2 × 13/5 × 13 = 26/65

Step 3: Add the Numerators
Now add the numerators (20 + 26 = 46) and keep the common denominator 65 unchanged.
Working: 20 + 26/65 = 46/65

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 46 and 65 is 1, confirming that 46/65 cannot be reduced further—it is already in its simplest irreducible form.
Working: 46/65

Step 5: Decimal & Percentage Representation
Dividing the numerator 46 by denominator 65 produces a repeating decimal (approximately 0.707692, or 70.7692%).
Working: 46 ÷ 65 = 0.707692 (70.7692%)

Key Values:
- Simplified Fraction: 46/65
- Mixed Number Form: 46/65
- Decimal Value: 0.707692
- Percentage: 70.7692%

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Solved with FractionsCalc:
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4/13 + 2/5 = 46/65

Simplified Fraction

46/65

Mixed Number

Proper (46/65)

Decimal Value

0.707692

Percentage

70.7692%

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Step-by-Step Solution: 4/13 + 2/5

Step 1

Find the Least Common Denominator (LCD)

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

LCD(13, 5) = 65

Step 2

Convert to Equivalent Fractions with Common Denominator 65

Multiply the numerator and denominator of 4/13 by 5, and multiply the numerator and denominator of 2/5 by 13 so both fractions share the common base 65.

4 × 5/13 × 5 = 20/65 and 2 × 13/5 × 13 = 26/65

Step 3

Add the Numerators

Now add the numerators (20 + 26 = 46) and keep the common denominator 65 unchanged.

20 + 26/65 = 46/65

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 46 and 65 is 1, confirming that 46/65 cannot be reduced further—it is already in its simplest irreducible form.

46/65

Step 5

Decimal & Percentage Representation

Dividing the numerator 46 by denominator 65 produces a repeating decimal (approximately 0.707692, or 70.7692%).

46 ÷ 65 = 0.707692 (70.7692%)

Visual Representation

The diagram below illustrates 4/13 plus 2/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`46/65`
Mixed Number Form	`46/65`
Decimal Form	`0.707692`
Percentage	`70.7692%`

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Frequently Asked Questions

What is 4/13 plus 2/5 as a fraction?

4/13 + 2/5 in simplest fraction form is 46/65.

What is 4/13 plus 2/5 as a decimal?

4/13 + 2/5 converted to a decimal is 0.707692.

What is 4/13 plus 2/5 as a percentage?

4/13 + 2/5 expressed as a percentage is 70.7692%.

Does 4/13 plus 2/5 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.707692...) because the denominator contains prime factors other than 2 and 5.