What is 2/5 plus 13/23? (Answer: 111/115)

Exact Answer

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Problem: What is 2/5 plus 13/23?
Formula / Expression: 2/5 + 13/23
Final Answer: 111/115
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 5 and 23 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 23 = 115.
Working: LCD(5, 23) = 115

Step 2: Convert to Equivalent Fractions with Common Denominator 115
Multiply the numerator and denominator of 2/5 by 23, and multiply the numerator and denominator of 13/23 by 5 so both fractions share the common base 115.
Working: 2 × 23/5 × 23 = 46/115 and 13 × 5/23 × 5 = 65/115

Step 3: Add the Numerators
Now add the numerators (46 + 65 = 111) and keep the common denominator 115 unchanged.
Working: 46 + 65/115 = 111/115

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 111 and 115 is 1, confirming that 111/115 cannot be reduced further—it is already in its simplest irreducible form.
Working: 111/115

Step 5: Decimal & Percentage Representation
Dividing the numerator 111 by denominator 115 produces a repeating decimal (approximately 0.965217, or 96.5217%).
Working: 111 ÷ 115 = 0.965217 (96.5217%)

Key Values:
- Simplified Fraction: 111/115
- Mixed Number Form: 111/115
- Decimal Value: 0.965217
- Percentage: 96.5217%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-5-plus-13-23/
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2/5 + 13/23 = 111/115

Simplified Fraction

111/115

Mixed Number

Proper (111/115)

Decimal Value

0.965217

Percentage

96.5217%

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Step-by-Step Solution: 2/5 + 13/23

Step 1

Find the Least Common Denominator (LCD)

The denominators 5 and 23 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 23 = 115.

LCD(5, 23) = 115

Step 2

Convert to Equivalent Fractions with Common Denominator 115

Multiply the numerator and denominator of 2/5 by 23, and multiply the numerator and denominator of 13/23 by 5 so both fractions share the common base 115.

2 × 23/5 × 23 = 46/115 and 13 × 5/23 × 5 = 65/115

Step 3

Add the Numerators

Now add the numerators (46 + 65 = 111) and keep the common denominator 115 unchanged.

46 + 65/115 = 111/115

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 111 and 115 is 1, confirming that 111/115 cannot be reduced further—it is already in its simplest irreducible form.

111/115

Step 5

Decimal & Percentage Representation

Dividing the numerator 111 by denominator 115 produces a repeating decimal (approximately 0.965217, or 96.5217%).

111 ÷ 115 = 0.965217 (96.5217%)

Visual Representation

The diagram below illustrates 2/5 plus 13/23 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`111/115`
Mixed Number Form	`111/115`
Decimal Form	`0.965217`
Percentage	`96.5217%`

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Frequently Asked Questions

What is 2/5 plus 13/23 as a fraction?

2/5 + 13/23 in simplest fraction form is 111/115.

What is 2/5 plus 13/23 as a decimal?

2/5 + 13/23 converted to a decimal is 0.965217.

What is 2/5 plus 13/23 as a percentage?

2/5 + 13/23 expressed as a percentage is 96.5217%.

Does 2/5 plus 13/23 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.965217...) because the denominator contains prime factors other than 2 and 5.