What is 8/23 plus 2/5? (Answer: 86/115)

Exact Answer

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Problem: What is 8/23 plus 2/5?
Formula / Expression: 8/23 + 2/5
Final Answer: 86/115
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 115
Multiply the numerator and denominator of 8/23 by 5, and multiply the numerator and denominator of 2/5 by 23 so both fractions share the common base 115.
Working: 8 × 5/23 × 5 = 40/115 and 2 × 23/5 × 23 = 46/115

Step 3: Add the Numerators
Now add the numerators (40 + 46 = 86) and keep the common denominator 115 unchanged.
Working: 40 + 46/115 = 86/115

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 86 and 115 is 1, confirming that 86/115 cannot be reduced further—it is already in its simplest irreducible form.
Working: 86/115

Step 5: Decimal & Percentage Representation
Dividing the numerator 86 by denominator 115 produces a repeating decimal (approximately 0.747826, or 74.7826%).
Working: 86 ÷ 115 = 0.747826 (74.7826%)

Key Values:
- Simplified Fraction: 86/115
- Mixed Number Form: 86/115
- Decimal Value: 0.747826
- Percentage: 74.7826%

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Solved with FractionsCalc:
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8/23 + 2/5 = 86/115

Simplified Fraction

86/115

Mixed Number

Proper (86/115)

Decimal Value

0.747826

Percentage

74.7826%

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Step-by-Step Solution: 8/23 + 2/5

Step 1

Find the Least Common Denominator (LCD)

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

LCD(23, 5) = 115

Step 2

Convert to Equivalent Fractions with Common Denominator 115

Multiply the numerator and denominator of 8/23 by 5, and multiply the numerator and denominator of 2/5 by 23 so both fractions share the common base 115.

8 × 5/23 × 5 = 40/115 and 2 × 23/5 × 23 = 46/115

Step 3

Add the Numerators

Now add the numerators (40 + 46 = 86) and keep the common denominator 115 unchanged.

40 + 46/115 = 86/115

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 86 and 115 is 1, confirming that 86/115 cannot be reduced further—it is already in its simplest irreducible form.

86/115

Step 5

Decimal & Percentage Representation

Dividing the numerator 86 by denominator 115 produces a repeating decimal (approximately 0.747826, or 74.7826%).

86 ÷ 115 = 0.747826 (74.7826%)

Visual Representation

The diagram below illustrates 8/23 plus 2/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`86/115`
Mixed Number Form	`86/115`
Decimal Form	`0.747826`
Percentage	`74.7826%`

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Frequently Asked Questions

What is 8/23 plus 2/5 as a fraction?

8/23 + 2/5 in simplest fraction form is 86/115.

What is 8/23 plus 2/5 as a decimal?

8/23 + 2/5 converted to a decimal is 0.747826.

What is 8/23 plus 2/5 as a percentage?

8/23 + 2/5 expressed as a percentage is 74.7826%.

Does 8/23 plus 2/5 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.747826...) because the denominator contains prime factors other than 2 and 5.